ICMA VI: The Sixth International - Arizona State...
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Transcript of ICMA VI: The Sixth International - Arizona State...
ICMA VI: The Sixth International Conference on Mathematical Modeling
and Analysis of Populations in Biological Systems
Held October 20 - 22, 2017, at the University of Arizona Tucson, Arizona, USA
Organizing Committee: J. M. Cushing (chair), University of Arizona Linda Allen, Texas Tech University, Lubbock Saber Elaydi, Trinity University, San Antonio Yun Kang, Arizona State University Joceline Lega, University of Arizona Jia Li, University of Alabama in Huntsville Hal Smith, Arizona State University Joe Watkins, University of Arizona
Scientific Advisory Committee: Fred Brauer, Mathematics Department, University of British Columbia J. M. Cushing, Department of Mathematics, University of Arizona Shandelle Henson, Department of Mathematics, Andrews University Mark Lewis, Centre for Mathematical Biology, University of Alberta Michael Neubert, Woods Hole Oceanographic Institution Scott Saleska, Ecology & Evolutionary Biology Department, University of Arizona
Supporters and Sponsors: Department of Mathematics, University of Arizona Department of Ecology & Evolutionary Biology, University of Arizona Simon A. Levin Mathematical, Computational & Modeling Sciences Center, Arizona State University The National Science Foundation, program in Mathematical Biology Taylor & Francis Group and the Journal of Biological Dynamics Interdisciplinary Program in Applied Mathematics, University of Arizona
BRIEF SCHEDULE Talks are held in rooms S107, S210, S215, S225 in the Environment and Natural Resources 2 building
FRIDAY (October 20) 8:45 - 9:00a: Welcoming Remarks (S107) 9:00 - 10:00a: Plenary Talk (S107) – Rosie Fisher
10:15 - 12:15p: Session 01 (S210): Michael Neubert, Mark Lewis, Amy Veprauskas, Ivan Sudakov Session 02 (S215): A.-A. Yakubu, Fred Brauer, Marisa Eisenberg Session 03 (S225): Zhijun Wu, Roger Nisbet, Theodore Galanthay
12:15 - 1:30p: Lunch break (on your own) 1:30 - 3:00p: Session 04 (S210): Patrick De Leenheer, Yang Kuang, Alex Farrell Session 05 (S215): Julien Arino, Linda Allen, Pauline van den Driessche Session 06 (S225): Tom Banks, Komi Messan, Marisabel Rodriguez
3:15 - 4:15p: Plenary talk (S107) – Mercedes Pascual
4:30 - 6:00p: Session 07 (S210): Joanna Masel, Peter Chesson, Paul Salceanu Session 08 (S215): Fabio Milner, Li Guan, Heidi Brown Session 09 (S225): Azmy Ackleh, Fan Bai, Hayriye Gulbudak
6:15 - 7:15p: Poster session (atrium)
SATURDAY (October 21) 8:45 - 9:00a: Horst Thieme: Homage to Karl-Peter Hadeler (S107) 9:00 - 10:00a: Plenary Talk (S107) – Henri Berestycki 10:15 - 12:15p: Session 10a (S107): Wenjing Zhang, Nafiu Hussaini Session 10b (S210): Yun Kang, Brian Dennis, Julie Blackwood, Greg Dwyer Session 11 (S215): Maia Martcheva, Nakul Chitnis, Lauren Childs, Abba Gumel Session 12 (S225): Hal Smith, Elena Braverman, Sophia Jang, Bingtuan Li
12:15 - 1:30p: Lunch break (on your own)
2:30 - 3:30p: Plenary talk (S107) – Regis Ferriere
3:50 - 5:20p: Session 13 (S107): Zhilan Feng, Frithjof Lutscher, Adam Lampert Session 14 (S210): Michael Doebeli, Paul Nelson, Jason Bertram Session 15 (S215): Horst Thieme, Yang Li, Melody Walker Session 16 (S225): Saber Elaydi, Wandi Ding, Vrushali Bokil
5:30 - 7:00p: Session 17 (S107): Xingfou Zou, Junping Shi, Holly Moeller Session 18 (S210): Shigui Ruan , Jianhong Wu, Necibe Tuncer Session 19 (S215): Cameron Browne, Weston Roda, John Nagy Session 20 (S225): Xueying Wang, Eva Stadler, Rebecca Tyson
SUNDAY (October 22) 9:00 - 10:00a: Featured Talk (S107) – Michael Kelly
10:15 - 12:15p: Session 21 (S210): Kaitlyn Martinez, Naveen Vaidya, Alhaji Cherif Session 22 (S215): Evan Milliken, Tracy Stepien, Glenn Ledder, Wei Lin Session 23 (S225): Judith Miller, Martha Garlick, Feng Rao, D.K.K. Vamsi
SCHEDULE OF TALKS
FRIDAY MORNING (October 20) 9:00 - 10:00a: Plenary Talk (S107) – Vegetation demographic models in Earth Systems Models Rosie Fisher, National Center for Atmospheric Research Climate & Global Dynamics, Boulder, CO
Session 01 (S210) 10:15 - 10:45a: Climate change and the bloom dynamics of a coastal phytoplankter Michael Neubert, Woods Hole Oceanographic Institution, Woods Hole, MA 10:45 - 11:15p: Genetic consequences of range expansion under climate change Mark Lewis, Department of Biological Sciences & the Department of Mathematical and Statistical Sciences,
University of Alberta, Edmonton, Canada 11:15 - 11:45a: Examining the dynamic consequences of evolution in response to a prolonged environmental
disturbance Amy Veprauskas, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 11:45 - 12:15p: Extinctions in Large Populations under Periodic and Chaotic Environmental Forcing Ivan Sudakov, Department of Physics, University of Dayton, Dayton, OH
Session 02 (S215) 10:15 - 10:45a: Disease Extinction Versus Persistence in Discrete-time Epidemic Models A.-A. Yakubu, Department of Mathematics, Howard University, Washington DC 10:45 - 11:15a: 11:15 - 11:45a: An epidemic model with superspreaders Fred Brauer, Department of Mathematics, University of British Columbia, Vancouver, Canada 11:45 - 12:15p: Connecting models with data: identifiability and uncertainty in modeling disease dynamics Marisa Eisenberg, Departments of Epidemiology & Mathematics, University of Michigan, Ann Arbor, MI
Session 03 (S225) 10:15 - 10:45a: Evolution of Social Cooperation of Microorganisms Zhijun Wu, Department of Mathematics, Iowa State University, Ames, IA 10:45 - 11:15a: Evolution and Regulation of Syntrophic Symbiosis Roger Nisbet, University of California, Santa Barbara, CA 11:15 - 11:45a: A game-theoretic approach to modeling ecological dynamics Theodore Galanthay, Ithaca College, Ithaca, NY
FRIDAY AFTERNOON (October 20)
Session 04 (S210) 1:30 - 2:00p: Tragedy of the commons in the chemostat Patrick De Leenheer, Department of Mathematics, Oregon State University, Corvallis, OR 2:00 - 2:30p: Rich Dynamics of a Stoichiometric Food Chain Model with Two Limiting Nutrients Yang Kuang, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 2:30 - 3:00p: Prey-Predator-Parasite: An Ecosystem Model With Fragile Persistence Alex Farrell, Department of Mathematics, N. C. State University, Raleigh, NC
Session 05 (S215) 1:30 - 2:00p: Duration of the stochastic phase of an epidemic Julien Arino, Department of Mathematics, University of Manitoba, Winnipeg, Canada 2:00 - 2:30p: The Duration of a Minor Epidemic in Stochastic Models of Infectious Diseases Linda Allen, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 2:30 - 3:00p: Model of Bovine Babesiosis in Cattle Pauline van den Driessche, Department of Mathematics and Statistics, University of Victoria, Canada
Session 06 (S225) 1:30 - 2:00p: Modeling Bumble Bee Population Dynamics with Delay Differential Equations Tom Banks, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC 2:00 - 2:30p: Population Dynamics of the Honeybee-mite Interactions Komi Messan, Simon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State
University, Tempe, AZ 2:30 - 3:00p: Population and vitellogenin dynamics of a honeybee colony influencing division of labor Marisabel Rodriguez, School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 3:15 - 4:15p: Plenary talk (S107) – Untangling the population dynamic interactions between climate and
infectious diseases Mercedes Pascual, Department of Ecology and Evolution, University of Chicago, Chicago, IL
Session 07 (S210) 4:30 - 5:00p: Individuals are discrete and it matters: an example using the lottery model Joanna Masel, Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 5:00 - 5:30p: Nonstationary Community Theory Peter Chesson, Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 5:30 - 6:00p: Competitive outcomes of a double-structured model of two invasive species of mollusks: zebra
and quagga mussel Paul Salceanu, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA
Session 08 (S215) 4:30 - 5:00p: Structured population model with diffusion in structure space Fabio Milner, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 5:00 - 5:30p: How the distribution for the time since infection to recovery affects the course of an epidemic Li Guan, Department of Mathematics, Tulane University, New Orleans, LA 5:30 -6:00p: Transdisciplinary network-based infectious disease modeling Heidi Brown, Department of Epidemiology and Biostatistics, University of Arizona, Tucson, AZ
Session 09 (S225) 4:30 - 5:00p: Disparate Disease Outcomes in Chronic Infection: the Role of Intra-Host Variability Azmy Ackleh, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 5:00 - 5:30p: The Effect of Delay in Viral Production in Within-Host Models during Early Infection Fan Bai, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 5:30 -6:00p: Modeling Distinct Virus Infection Strategies in Virus-Microbe Systems Hayriye Gulbudak, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana
SATURDAY MORNING (October 21)
8:45 - 9:00a: Homage to Karl-Peter Hadeler (S107), Horst Thieme 9:00 - 10:00a: Plenary Talk (S107) – Predators-prey model with competition: emergence of territoriality and
packs in animal behavior Henri Berestycki, EHESS, PSL University, Paris, France
Session 10a (S107) 10:15 – 1045a: Dynamical Analysis on an Autoimmune Disease Model via Model Reduction Wenjing Zhang, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 10:45 - 11:15a: Temperature-dependent Model for the Dynamics of Zoonotic Visceral Leishmaniasis in Human
and Animal Reservoir Populations Nafiu Hussaini, Bayero University Kano, P.M.B. 3011, Kano, Nigeria
Session 10b (S10) 10:15 - 10:45a: Dynamics of Hierarchy Establishment from Nonlinear Social Interactions and Metabolic Costs Yun Kang, Science and Mathematics Faculty College of Integrative Sciences and Arts, Arizona State
University, Mesa, AZ 10:45 - 11:15a: Analytical expressions for the eigenvalues and other quantities arising from a 3-stage wildlife
population matrix Brian Dennis, Department of Fish and Wildlife Sciences, University of Idaho, Moscow, Idaho 11:15 - 11:45a: Uncovering the drivers of spatial synchrony of periodical cicadas in the U.S. Julie Blackwood, Department of Mathematics and Statistics, Williams College, Williamstown, MA 11:45 - 12:15p: Combining Models and Data to Understand the Mechanisms Driving Insect Outbreaks Greg Dwyer, Department of Ecology & Evolution, University of Chicago, Chicago, Illinois
Session 11 (S215) 10:15 - 10:45a: How does within-host dynamics affect population-level dynamics? Insights from an immuno-
epidemiological model of malaria Maia Martcheva, Department of Mathematics, University of Florida, Gainesville, FL 10:45 - 11:15a: Transmission Dynamics of Opisthorchis viverrini Nakul Chitnis, Swiss Tropical and Public Health Institute, Basel, Switzerland 11:15 - 11:45a: The Impact of Within-Vector Dynamics on Malaria Parasite Diversity Lauren Childs, Department of Mathematics, Virginia Tech, Blacksburg, VA 11:45 - 12:15p: Effect of temperature on the dynamics of malaria vector and disease: a theoretical analysis Abba Gumel, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ
Session 12 (S225) 10:15 - 10:45a: Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model
of cell migration Hal Smith, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 10:45 - 11:15a: Lotka systems with directed dispersal dynamics: competition and influence of diffusion strategies Elena Braverman, Department of Mathematics, University of Calgary, Calgary, Alberta, Canada 11:15 - 11:45a: Dynamics of a population in two patches with dispersal Sophia Jang, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 11:45 - 12:15p: Complex Spatial Dynamics in Integro-Difference Equations Bingtuan Li, Department of Mathematics, University of Louisville, Louisville, KY
SATURDAY AFTERNOON (October 21) 2:30 - 3:30p: Plenary talk (S107) – Ecological interactions, evolutionary adaptation, and the dynamics of neutral
genetic diversity Regis Ferriere, Department of Ecology and Evolutionary Biology Department, University of Arizona
Session 13 (S107)
3:50 - 4:20p: Plant toxins and trophic cascades alter fire regime and succession on a boreal forest landscape Zhilan Feng, Department of Mathematics, Purdue University, West Lafayette, IN 4:20 - 4:50p: How predator behavior and seasonality affect predator-prey dynamics Frithjof Lutscher, Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada 4:50 - 5:20p: Three paradoxical results for ecosystem management by multiple agents Adam Lampert, School of Human Evolution and Social Change and Mathematical, Computational and
Modeling Science Center, Arizona State University, Tempe, AZ
Session 14 (S210)
3:50 - 4:20p: From individual-based birth-death processes to macro-evolutionary patterns Michael Doebeli, Departments of Biology and Mathematics, University of British Columbia, Canada 4:20 - 4:50p: Somatic evolution and aging in multicellular organisms Paul Nelson, Department of Ecology & Evolutionary Biology, University of Arizona, Tucson, AZ 4:50 - 5:20p: Feedbacks can drive large fluctuations in adaptation rates Jason Bertram, Department of Ecology & Evolutionary Biology, University of Arizona, Tucson, AZ
Session 15 (S215)
3:50 - 4:20p: Can infectious pathogens drive their host populations into extinction? Horst Thieme, Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 4:20 - 4:50p: Discrete-time Structured Model for Malaria Transmission with constant releasing sterile
mosquitoes Yang Li, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 4:50 - 5:20p: Modeling allele effects in a transgenic mosquito population during range expansion Melody Walker, Mathematics Department, Virginia Tech, Blacksburg, VA
Session 16 (S225) 3:50 - 4:20p: A Discrete Mathematical Model for the Aggregation of β-Amyloid Saber Elaydi, Department of Mathematics, Trinity University, San Antonio, TX 4:20 - 4:50p: Mathematical Models of Community-acquired and Hospital-acquired Methicillin-resistant
Staphylococcus Aureus (MRSA) transmission in Hospital and Community Settings Wandi Ding, Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 4:50 - 5:20p: Modeling and Control of Vector Transmitted Viral Disease of Crops with Different Replanting
Strategies Vrushali Bokil, Department of Mathematics, Oregon State University, Corvallis, OR
Session 17 (S107) 5:30 - 6:00p: Modelling the fear effect in predator-prey interactions with adaptive avoidance of predators Xingfou Zou, Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada 6:00 - 6:30p: A mathematical model of interaction of pelagic algae, benthic algae and nutrients in an oligotrophic
shallow aquatic ecosystem Junping Shi, Department of Mathematics, College of William and Mary, Williamsburg, VA 6:30 - 7:00p: Acquired metabolism as an evolutionary path to mixotrophy Holly Moeller, Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA
Session 18 (S210) 5:30 - 6:00p: Modeling the Importation and Local Transmission of Zika in Florida Shigui Ruan, Department of Mathematics, University of Miami, Coral Gables, FL 6:00 - 6:30p: Zika and dengue: the optimal vaccination rate when antibody enhancement considered Jianhong Wu, Laboratory for Industrial and Applied Mathematics, York University, Canada 6:30 - 7:00p: Structural and Practical Identifiability Analysis of Zika Epidemiological Models Necibe Tuncer, Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL
Session 19 (S215) 5:30 - 6:00p: Dynamics of Virus and Immune Response Network Models Cameron Browne, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 6:00 - 6:30p: Modeling lentiviral infection and viral latency in the brain during antiretroviral therapy Weston Roda, Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, Canada 6:30 - 7:00p: A model of natural selection predicts treatment resistance in prostate cancer John Nagy, Department of Life Sciences, Scottsdale Community College & the School of Mathematical and
Statistical Sciences, Arizona State University, Tempe, AZ
Session 20 (S225) 5:30 - 6:00p: Impact of bacterial hyperinfectivity on cholera epidemics in spatially heterogeneous environments Xueying Wang, Department of Mathematics, Washington State University, Pullman, WA 6:00 - 6:30p: Travelling waves in a model for the growth of Phytophthora Eva Stadler, Department of Mathematics, Technical University of Munich, Germany 6:30 - 7:00p: Understanding the Dynamics of Opinions in a Fully-Mixed Population Rebecca Tyson, Department of Mathematics, University of British Columbia Okanagan, Kelowna, Canada
SUNDAY MORNING (October 22) 9:00 - 10:00a: Featured talk (S107) – The impact of spatial arrangements on disease dynamics and intervention
strategies Michael Kelly, Department of Mathematics, Transylvania University, Lexington, KY
Session 21 (S210) 10:15 - 10:45a: Methods for Parameter Estimation of a Stochastic SEIR Model using Bayesian Inference Kaitlyn Martinez, Applied Mathematics & Statistics, Colorado School of Mines, Golden 10:45 - 11:15a: Impact of Spatially Heterogeneous Temperature on Dengue Epidemics Naveen Vaidya, Department of Mathematics and Statistics, San Diego State University, California 11:15 - 11:45a: Strain structures in a multi-locus-allele epidemic model with age-structures for pathogens with
variable antigenic forms Alhaji Cherif, School of Mathematical and Statistical Sciences, Arizona State University and Renal Research
Institute, New York Session 22 (S215)
10:15 - 10:45a: A Technique to Approximate Hitting Probabilities with Applications to Metapopulation Models Evan Milliken, School of Mathematical and Statistical Science, Arizona State University, Tempe 10:45 – 11:15a: Modeling the Migration of Astrocytes During Retinal Development Tracy Stepien, Department of Mathematics, University of Arizona, Tucson, Arizona 11:15 - 11:45a: A Mathematical Model for Onchocerciasis with Intermittent Treatment Glenn Ledder, Department of Mathematics, University of Nebraska-Lincoln 11:45 - 12:15p: Adaptive desynchronization and synchronization in coupled biological oscillators Wei Lin, School of Mathematical Sciences & Institute of Science and Technology for Brain-Inspired
Intelligence, Fudan University, Shanghai, China
Session 23 (S225) 10:15 - 10:45a: Spatial models of population dynamics and quantitative traits Judith Miller, Department of Mathematics & Statistics, Georgetown University, Washington DC 10:45 - 11:15a: Using Homogenization to Estimate Random-Walk Motility from Telemetry Data in
Heterogeneous Landscapes Martha Garlick, Mathematics & Computer Science, South Dakota School of Mines & Technology, Rapid City 11:15 - 11:45a: The complex dynamics of a diffusive prey-predator model with an Allee effect in prey Feng Rao, Nanjing Tech University, China 11:45 - 12:15p: Rich dynamics exhibited by predator-prey systems provided with additional food supplements in
the presence of inhibitory effect: Applications to pest control D.K.K. Vamsi, Department of Mathematics & Computer Science, Sri Sathya Sai Institute of Higher Learning,
Prasanthinilayam, India
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Plenary Talks
1
Predators-prey model with competition: emergence of territorialityand packs in animal behavior
Henri Berestycki
EHESS, PSL University - Paris
Abstract: I report here on a series of joint works with Alessandro Zilio about systems of predators
interacting with a single prey. We consider predators like wolves that can divide into several hostile
packs. The questions are to understand the conditions under which predators segregate into packs,
whether there is an advantage to have such hostile packs, and to compare the various territory
configurations that arise in this context. Mathematically, we focus on the analysis of stationary
states, stability issues, and asymptotics of the system when the competition parameter becomes
unbounded.
2
Ecological interactions, evolutionary adaptation, and the dynamicsof neutral genetic diversity
Regis Ferriere
Institute of Biology, Ecole Normale Supérieure, Paris-Sciences-Lettres Research University
Department of Ecology and Evolutionary Biology, University of Arizona
Joint International Research Center iGLOBES, CNRS — University of Arizona
with Sylvain Billiard (Lille University), Sylvie Méléard (Ecole Polytechnique), and Chi Viet Tran
(Lille University)
Abstract: The science of biodiversity currently faces the challenge of understanding how ecolog-
ical processes shape evolutionary change, and reciprocally how evolution affects the structure and
function of ecological systems. Such “eco-evolutionary feedback” determine the dynamics of adap-
tive traits — quantitative characters that are heritable yet mutable from parent to offspring. While
eco-evolutionary feedbacks can result in variation of adaptive traits among populations, much of the
molecular diversity measured in populations involve DNA sequences that are selectively neutral. A
neutral sequence that is physically linked in the genome to the sequence that codes for the adaptive
trait is called a marker of that trait. A longstanding question in evolutionary theory is under-
standing how variation in such molecular markers evolves, and how patterns of neutral molecular
evolution can be used to infer the history of adaptive trait evolution. We address these questions
by developing a mathematical framework for finite population dynamics in continuous time, where
each individual is characterized by a trait under selection and a completely linked neutral marker.
Population dynamics are driven by births and deaths, mutations at birth, and competition be-
tween individuals. Trait values influence ecological processes (demographic events, competition),
and competition generates selection on trait variation, thus closing the eco-evolutionary feedback
loop. The demographic effects of the trait are also expected to influence the generation and main-
tenance of neutral variation. We consider a large population limit with rare mutation, under the
assumption that the neutral marker mutates faster than the trait under selection. We prove the
convergence of the stochastic individual-based process to a new measure-valued diffusive process
with jumps that we call Substitution Fleming-Viot Process (SFVP). We discuss the implications
of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary
feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint
importance of ecological interactions in the restoration of neutral diversity after a selective sweep.
3
Vegetation demographic models in Earth Systems Models
Rosie Fisher
National Center for Atmospheric Research Climate & Global Dynamics,
Boulder, CO, USA
Abstract: Earth System Models (ESMs), which are used to understand past and present climate
regimes, and to predict future climate trajectories, now include detailed simulations of the terrestrial
biosphere. These terrestrial biosphere models mediate land-atmosphere energy and water exchange,
as well as the long-term interaction of atmospheric CO2 with soil and vegetation carbon stocks,
and the movement of biome boundaries in response to climate shifts. In the past, such models
had relatively simplistic representations of plant carbon pools, often with no consideration of plant
populations at all. A new class of vegetation demographic models is now being incorporated
into ESMs, which allow plant populations and community assembly processes to emerge from
the physiological specifications of competing plant types. This brings the theoretical ecology of
coexistence into the remit of climate projection, as well as providing a set of tools for testing our
fundamental understanding of the mechanistic underpinning of plant biogeography. Here I discuss
the state of the science in this arena, and highlight issues raised so far that could benefit from
stronger interactions with the ecological and population modeling communities.
4
Untangling the population dynamic interactions between climate andinfectious diseases
Mercedes Pascual
Department of Ecology and Evolution, University of Chicago, Chicago, Illinois, USA
Abstract: Framed within the recurrent dichotomy of extrinsic drivers vs. intrinsic (nonlinear)
dynamics, my talk presents a series of case studies and modeling approaches addressing the role of
climate forcing in the context of the population dynamics of infectious diseases. I start with the
temporal dynamics of diarrheal infections in Bangladesh, both cholera and rotavirus, and the role
of The El Niño Oscillation and flooding. This work illustrates the combination of process-based
mathematical models of transmission and statistical inference methods for nonlinear stochastic
systems, to interrogate time series from epidemiological surveillance about climate variability. I then
illustrate challenges that arise in spatio-temporal transmission dynamics within urban environments
of the developing world. In a second part, I consider another major class of climate-sensitive
diseases, those caused by vector-borne infections, and present results on epidemic malaria at the
edge of the geographic distribution of the disease, in arid regions of India and highlands of East
Africa. I close with some future directions that should replace old dichotomies.
5
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Featured Speakers
co-Winners of the Lord Robert May Best Paper Prize
Journal of Biological Dynamics 2015-2016
6
The impact of spatial arrangements on disease dynamicsand intervention strategies
Michael Kelly
Department of Mathematics, Transylvania University
Lexington, Kentucky
Abstract: The role of spatial arrangements on the spread of and management strategies for
waterborne diseases is investigated. In particular, we consider questions of optimal vaccination
distributions on heterogeneous community networks, both in response to and preemptively before
a cholera outbreak. Metapopulation models are at the foundation of our work, incorporating a
susceptible-infected-recovered system coupled with a compartment modeling the concentration of
Vibrio cholerae in aquatic reservoirs. Using optimization methods, we seek to answer questions on
how best to minimize the number of infected individuals during an outbreak, minimize the risk of
an outbreak, and minimize the associated cost of intervention. Simulations are shown for varying
scenarios and networks, and results provide guidance on where to prioritize vaccination in light of
outbreaks.
7
A new approach for designing disease intervention strategiesin metapopulation models
Diana Knipl1
MTA-SZTE Analysis and Stochastic Research Group, University of Szeged
Szeged, Hungary
Abstract: We describe a new approach for investigating the control strategies of compartmental
disease transmission models. The method rests on the construction of various alternative next-
generation matrices, and makes use of the type reproduction number and the target reproduction
number. A general metapopulation SIRS (susceptible-infected-recovered-susceptible) model is given
to illustrate the application of the method. Such model is useful to study a wide variety of diseases
where the population is distributed over geographically separated regions. Considering various
control measures such as vaccination, social distancing, and travel restrictions, the procedure al-
lows us to precisely describe in terms of the model parameters, how control methods should be
implemented in the SIRS model to ensure disease elimination. In particular, we characterize cases
where changing only the travel rates between the regions is sufficient to prevent an outbreak.
1Due to unfortunate travel disruptions, Dr. Knipl was unable to attend the conference.
8
Invited and Contributed Talks
Disparate Disease Outcomes in Chronic Infection: the Role ofIntra-Host Variability
Azmy S. Ackleh
University of Louisiana at Lafayette
Keywords: Disease progression variability, Intra-host model, Mycobacterium marinum, Physio-
logically structured models
Abstract: We recently developed a model for the transmission of Mycobacterium marinum (Mm)
in aquatic animals. This model is structured by bacterial load within host. Mm is a close genetic
relative to the bacterium that causes human TB, and affects marine mammals on the same scale
and with similarly varied disease presentation. It is evident that for a mathematical model to agree
with laboratory infection studies and common observations, it is necessary to address the disparate
outcomes explicitly, namely, the large pool of chronically but asymptomatically infected individuals,
and individuals with acute infections. In this talk, we first present a second order numerical scheme
for computing model solutions and prove its convergence to the weak solution of the model. Then
we demonstrate that we can improve upon the agreement between the model and data by taking a
simpler (fewer cohorts of fish), but more biologically meaningful modeling approach. We briefly also
demonstrate that this phenomenological approach, particularly in conjunction with experiments,
may be useful to provide support for or against hypotheses of underlying processes governing disease
progression.
10
The Duration of a Minor Epidemic in Stochastic Models ofInfectious Diseases
Linda J. S. Allen
Texas Tech University
Keywords: Markov chain, branching process, infectious disease
Abstract: Public health intervention and control strategies are designed to shorten the course of
an epidemic. This is often achieved through reduction of the basic reproduction number R0 toa value below the critical threshold of one. We apply continuous-time Markov chain models and
branching process approximations to investigate the time to disease extinction, assuming extinction
occurs. Explicit formulas for the moments for time to extinction are computed. As R0 approachesone, the probability of disease extinction increases but the time until extinction also increases.
We illustrate this increase in time to disease extinction, near the critical threshold of R0 = 1, in
several epidemic models. These results have implications for public health intervention and control
strategies.
11
Duration of the stochastic phase of an epidemic
Julien Arino
Department of Mathematics, University of Manitoba
Winnipeg, Manitoba R3T 2N2, Canada
Abstract: Before they become full blown, epidemics go through a phase during which they undergo
stochastic oscillations. During this phase, they might also die out before having any significant
impact. In order to study the duration of this phase, we consider a variation on a simple random
walk model of Allen to incorporate two absorbing states. We then extend the model to two locations
to consider whether this has an effect on the duration and likelihood of an outbreak.
12
The Effect of Delay in Viral Production in Within-Host Modelsduring Early Infection
Fan Bai
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas
Keywords: Markov chain, probability of extinction, stochastic differential equation, viral infection
Abstract: Delay in viral production may have a significant impact on the early stages of infection.
During the eclipse phase, the time from viral entry until active production of viral particles, no
viruses are produced. This delay affects the probability of viral emergence. Deterministic and
stochastic models are formulated with either multiple latent stages or a fixed delay for the eclipse
phase. The deterministic model with multiple latent stages approaches in the limit a model with a
fixed delay as the number of stages approaches infinity. The basic reproduction number is defined for
each of the deterministic models. Generalization of the deterministic models to stochastic models
allows estimation of the probability of viral establishment from a branching process approximation
of the continuous-time Markov chain model and of the distribution for time to peak infection from
the stochastic differential equation models. The dynamics of the deterministic and stochastic models
are compared analytically and numerically. The impact of the delay on therapeutic interventions
is discussed.
13
Modeling Bumble Bee Population Dynamics with DelayDifferential Equations
H.T. Banks
Center for Research in Scientific Computation, N.C. State University,
Raleigh, N.C. 27695 USA
Abstract: We report on our continuing efforts between our group at NCSU and ecologists at
California State University, Monterey Bay and the Swedish University of Agricultural Sciences,
Uppsala. To provide a tool for projecting and testing sensitivity of growth and death of popula-
tions under contrasting and combined pressures, we developed a non-linear, non-autonomous delay
differential equation (DDE) model of bumblebee colonies and resources model that describes multi-
colony bumble bee population dynamics. We explain the usefulness of delay differential equations
as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a
specific spline-based numerical method that approximates the solution of the delay model. We
demonstrate that the model satisfies sufficient conditions to assure the subsequent theoretical de-
velopments therein in order to attain convergent approximate solutions. We report on our recent
efforts on studies of response to toxic substances, in particular our simulations related to growth,
death and sublethal responses to neonicotinoid exposure.
14
Feedbacks can drive large fluctuations in adaptation rates
Jason Bertram
University of Arizona
Keywords: evolution, statistical mechanics, nonlinear stability
Abstract: Evolution in the absence of genetic recombination (transfer of genetic material between
individuals) has rich and interesting “travelling wave” dynamics. Even enormous populations are
subject to the population dynamics and mutant production of the fittest individuals, which are
stochastic processes [1,2]. Stochastic fluctuations in this fittest subset are amplified by positive
feedbacks, so that the overall movement and shape of the traveling wave is intrinsically unstable over
much longer timescales than the stochastic fluctuations themselves [3]. We review these phenomena
and show that asexual travelling waves are even more unstable when there is a small amount of
genetic recombination, and that they exhibit adaptive “leaps”.
References
[1] M M Desai, and D S Fisher. Beneficial mutation-selection balance and the effect of linkage on
positive selection. Genetics 176.3 (2007): 1759-1798.
[2] S C Park, D Simon, and J Krug. The speed of evolution in large asexual populations. J. Stat. Phys.
138.1 (2010): 381-410.
[3] D S Fisher, Asexual evolution waves: fluctuations and universality. J. Stat. Mech.: Theory and
Experiment 2013.01 (2013): P01011.
15
Uncovering the drivers of spatial synchrony of periodicalcicadas in the U.S.
Julie Blackwood
Williams College
Keywords: Leslie matrix, periodical cicada, synchrony
Abstract: In addition to their unusually long life cycle, periodical cicadas provide an exceptional
example of synchronized life stage phenology in nature. Single broods (or age cohorts) span large
geographical regions ranging from 50,000 to 500,000 km2, and adults emerge synchronously every
13 or 17 years. The mechanisms driving the observation that only a single brood is normally
present in a given spatial location remain largely unknown. We develop non-linear Leslie matrix-
type models of periodical cicadas that include predation-driven Allee effects and competition in
addition to reproduction and survival. We use our models to lend insight into the driving forces
behind the observed spatial structure of periodical cicadas.
16
Modeling and Control of Vector Transmitted Viral Disease of Cropswith Different Replanting Strategies
Vrushali A. Bokil
Department of Mathematics, Oregon State University, Corvallis, OR 97331-4605, U.S.A.
Keywords:Vectored Disease, Plant Pathogens, SIS Model, Optimal Control, African Cassave Mo-
saic Virus
Abstract: Vector-transmitted diseases of plants have had devastating effects on agricultural pro-
duction worldwide, resulting in drastic reductions in yield for crops such as cotton, soybean, tomato
and cassava. In this investigation, we formulate a new plant-vector-virus model with continuous
replanting from density-dependent replanting of healthy and some infected plants. The new model
is an extension of a model formulated in [1] by Holt et al. Both models are analyzed and thresholds
for disease elimination are defined in terms of the model parameters. Parameter values for cassava,
whiteflies, and the virus, in African cassava mosaic virus serve as a case study. A numerical investi-
gation illustrates how the equilibrium densities of healthy and infected plants for both models vary
with changes in parameter values. Applications of insecticide and roguing to reduce plant disease
and to increase the number of plants harvested are studied using optimal control theory.
References
[1] J. Holt, M. J. Jeger, J. M. Thresh and GW Otim-Nape, An epidemiological model incorporating
vector population dynamics applied to African cassava mosaic virus disease, Journal of Applied
Ecology (1997), 793-806.
17
An epidemic model with superspreaders
Fred Brauer
Department of Mathematics, University of British Columbia,
Vancouver BC V6T 1Z2, Canada
Abstract: It appears that superspreading may be common in epidemics. We analyze a simple
compartmental model for superspreading, and there are indications that such a model produces
fewer disease cases than a simple homogeneous mixing model with the same reproduction number.
18
Lotka systems with directed dispersal dynamics: competitionand influence of diffusion strategies
Elena Braverman
University of Calgary, Canada
Keywords: Lotka system, dispersal strategy, ideal free distribution, ideal free pair, global attrac-
tivity, coexistence, competition, cooperation
Abstract: We study a (possibly Lotka) system describing two competing populations, and each of
them chooses its diffusion strategy as the tendency to have a distribution proportional to a certain
positive prescribed function. For instance, the standard diffusion corresponds to the choice of a
uniform distribution. We focused on the interplay of species competition and diffusion strategies
with some other factors incorporated: different growth rates, carrying capacities and harvesting.
We describe the cases when the choice of diffusion strategies promotes coexistence.
19
Transdisciplinary network-based infectious disease modeling
Heidi E. Brown
Department of Epidemiology and Biostatistics, University of Arizona
Keywords: network model, mosquito abundance, disease propagation, climate
Abstract: In 2013/14 mosquito-borne chikungunya spread through the Caribbean infecting more
than 3 million individuals. The following year, Zika similarly spread throughout the region. Between
island spread of chikungunya was shown to be associated with geographical proximity to an infected
island. An analysis of pandemic spread found that diseases propagated at uniform speeds when
Euclidean distance was replaced by a flow based network between cities. I will discuss the work our
transdisciplinary team has completed, downscaling a pandemic model to describe the propagation of
infection across the island nation of Dominica. In addition, I will discuss our work to integrate our
climate, geographic, epidemiologic and mathematical models into a single description of mosquito-
borne disease spread.
20
Dynamics of Virus and Immune Response Network Models
Cameron Browne
Department of Mathematics, University of Louisiana at Lafayette
Abstract: The dynamics of virus and immune response within a host can be viewed as a complex
and evolving ecological system. For example, during HIV infection, an array of CTL immune
response populations recognize specific epitopes (viral proteins) presented on the surface of infected
cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at
different epitopes, inducing a dynamic network of viral and immune response variants. We consider
models for the network of virus and immune response populations, consisting of Lotka-Volterra-like
systems of ordinary differential equations. Stability of several equilibria and uniform persistence
of distinct viral/immune variants are characterized utilizing a Lyapunov function. Our analysis
provides insights on viral immune escape from multiple epitopes. In the “binary mutation” setting,
we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the
system of 2 virus strains converges to a “perfectly nested network” with less than or equal to +1
persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength
of immune response to an epitope, is the most important factor determining the persistent network
structure.
21
Strain structures in a multi-locus-allele epidemic model withage-structures for pathogens with variable antigenic forms
Alhaji Cherif, D. Phil.
Renal Research Institute, New York, USA
School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA
Keywords: age-structured epidemic models, multi-strain, stability analysis, strain structures,
multi-locus-allele
Abstract: Understanding coexistence and maintenance of strain structure of antigenically vari-
able pathogens under cross-immunity mediated competitions have important implications for the
effectiveness of public health interventions, ranging from using strain composition for a vaccine
to the understanding emergence and/or reemergence of antigenically discordant subtypes. Here,
we provide rigorous analyses of the multi-locus-allele age-structured model to study pathogen-
specific dynamical patterns and age-specificity. Using fixed-point and spectral theory of operators,
we determine the persistence and extinction of all strains. In addition, we established addition
threshold-like quantities to determine both the dynamic patterns and maintenance of certain anti-
genic strain structures. As in [1, 2], we determine further threshold conditions needed for the system
to exhibit different strain structures. That is, under certain conditions, we observe the existence
of discrete antigenic forms among pathogens that can either fully or partially self-organize, where
strains exhibit no strain structures and co-exist, or antigenic variants sort into non-overlapping or
minimally-overlapping clusters that either undergo the principle of competitive exclusion exhibiting
discrete strain structures or co-exist cyclically. Understanding the regime in which these diverse
strain structures are maintained are fundamental to exploring the effectiveness of vaccine strain
composition, emergence and reemergence of new or discordant antigenic subtypes and are of utmost
importance to epidemiology and public health decision making.
References
[1] A. Cherif, Mathematical analysis of a multiple strain, multi-locus-allele system for antigenically
variable infectious diseases revisited. Mathematical Biosciences, 267 (2015) 24-40.
[2] A. Cherif, J. Dyson, P.K. Maini, and S. Gupta, An Age-structured multi-strain epidemic model
for antigenically diverse infectious diseases: A multi-locus framework. Nonlinear Analysis-Real
World Applications 34 (2017) 275-315.
22
Nonstationary Community Theory
Peter Chesson
University of Arizona
Keywords: nonstationary process, nonautonomous dynamics, scale transition theory, threshold
growth model, Beverton-Holt model, lottery model
Abstract: The study of the role of environmental variation in community dynamics has tradition-
ally assumed that the environment is a stationary stochastic process or a periodic deterministic
process. However, the physical environment in nature is nonstationary, which is reflected in nat-
ural communities that show long-term change. Anthropogenically driven climate change provides a
new challenge of directional change highly evident in the present, and emphasizes a persistent but
frequently ignored challenge: how to make predictions about the dynamics of communities when
the nonstationarity of the physical environment is recognized.
Recent work has pointed the way to drawing conclusions about community dynamics with none
of the traditional assumptions of environmental stationarity or periodicity [1]. Assumptions about
convergences of long-term averages of environmental states, so prevalent in studies in stationary
environments, can be replaced by assumptions about temporal sums of functions environmental
states with otherwise arbitrary environmental change. Combined with scale-transition theory [2],
powerful tools for understanding nonstationary community dynamics are available. These tools
will be illustrated with some simple models of nonstationary community dynamics including the
threshold growth model, the Beverton-Holt model and the lottery model.
References
[1] Chesson, P. 2017. AEDT: A new concept for ecological dynamics in the ever-changing world.
PLoS Biology 15(5): e2002634
[2] Li, L., Chesson, P. 2016. The effects of dynamical rates on species coexistence in a variable
environment: the paradox of the plankton revisited. The American Naturalist 188, E46-E58
23
The Impact of Within-Vector Dynamics on Malaria Parasite Diversity
Lauren M. Childs
Virginia Tech
Keywords: multi-scale model, malaria, parasite diversity, stochastic dynamics
Abstract: Plasmodium falciparum, the most virulent human malaria parasite, matures via asexual
reproduction within the human host, but undergoes sexual reproduction within its vector host, the
Anopheles mosquito. Consequently, the mosquito stage of the parasite life cycle provides an oppor-
tunity to create novel parasite genetic information in mosquitoes infected with multiple parasite
populations, altering parasite diversity at the population level. Despite the important implications
for disease transmission and malaria control, a quantitative mapping of diversity generation within
the vector is lacking. To examine the role that vector biology plays in modulating parasite diversity,
we develop a multi-scale model that estimates the diversity as a consequence of different bottlenecks
and expansion events occurring during the parasite life cycle and couples the diversity development
within the mosquito to transmission to humans. For the underlying framework, we use a stochastic
model of within-vector P. falciparum dynamics and simulate the dynamics of infections with mul-
tiple distinct parasite populations [1]. We use the output of the within-vector portion of our model
to inform transmission of the parasites to the human population. Our model quantitatively maps
parasite diversity through the life cycle of the parasite including bottlenecks between the mosquito
and the human host.
References
[1] L. M. Childs, O. F. Prosper, Simulating within-vector generation of the malaria parasite diversity,
PLoS ONE (2017): 12(5): e0177941.
24
Transmission Dynamics of Opisthorchis viverrini
Nakul Chitnis
Swiss Tropical and Public Health Institute
Keywords: opisthorhciasis, ordinary differential equations, partial differential equations, type-
reproduction numbers, intervention strategies
Abstract: The trematode liver fluke (flat worm), Opisthorchis viverrini, is prevalent in southeast
Asia, causing the chronic hepatobiliary disease, opisthorchiasis. We develop an ordinary differential
equation (ODE) model of the transmission dynamics of O. viverrini through its life cycle in snails,
fish, and humans; a second ODE model that includes potential transmission from reservoir hosts
such as domestic cats and dogs; and a third partial differential equation (PDE) model that includes
heterogeneity in age in humans. We calibrate these models to data collected from two communities
in Khong Island in Southern Lao PDR, using maximum likelihood estimates and Bayesian sampling-
resampling methods. We define basic reproduction numbers and type-reproduction numbers for
these models to show that humans can maintain the transmission cycle through snails and fish,
so interventions targeting humans with a sufficiently high coverage could eliminate transmission.
Numerical simulations suggest that, as compared to improved sanitation and behaviour change
campaigns, treating humans at least once a year increases the probability of achieving elimination
and reduces the time to elimination.
25
Tragedy of the commons in the chemostat
Patrick De Leenheer
Oregon State University
Keywords: tragedy of the commons, chemostat, cooperators and cheaters, evolution of cooperation.
Abstract: A proof of principle is presented for the phenomenon of the tragedy of the commons
that is at the center of many theories on the evolution of cooperation. Whereas the tragedy is
commonly set in a game theoretical context, and attributed to an underlying Prisoner’s Dilemma,
an alternative approach is taken here which is based on basic mechanistic principles of species growth
that does not rely on the specification of payoffs which may be difficult to determine in practice.
The tragedy is established in the context of a general chemostat model with two species, the
cooperator and the cheater. Both species have the same growth rate function and yield constants,
but the cooperator allocates a portion of the nutrient uptake towards the production of a public
good—the “Commons” in the Tragedy—which is needed to digest the externally supplied nutrient.
The cheater on the other hand does not produce this public good, and allocates all nutrient uptake
towards its own growth. It is proved that when the cheater is present initially, both the cooperator
and the cheater will eventually go extinct, hereby confirming the occurrence of the tragedy. It
is also shown that without the cheater, the cooperator can survive indefinitely, provided that at
least a low level of public good or processed nutrient is available initially. These results provide a
predictive framework for the analysis of cooperator-cheater dynamics in a powerful model system
of experimental evolution.
26
Analytical expressions for the eigenvalues and other quantitiesarising from a 3-stage wildlife population matrix
Brenda Hanley and Brian Dennis*
University of Idaho
Keywords: cubic polynomial solution, dominant eigenvalue, finite rate of population growth,
Lefkovitch matrix, Leslie matrix, population viability analysis, subdominant eigenvalue, stage-
structured population
Abstract: We used the well-known symbolic solution for the roots of a cubic polynomial to
derive expressions for the dominant and subdominant eigenvalues of a 3-stage population projection
matrix. As well, we obtained analytical expressions for matrix eigenvectors, complex moduli,
damping ratios, sensitivities, and elasticities. The projection matrix corresponds to any wildlife
population containing juvenile, subadult, and adult stages. In the characteristic equation, the 9
demographic parameters (fertilities and stage transition probabilities) collapse into no more than 3
superparameters. Eigenvalues and functions of eigenvalues can thus be calculated using at most 3
superparameters only, potentially simplifying data collection efforts for estimating growth rate and
demographic quantities. In the case of a common 3-stage life history in which only adults reproduce
and have a self-loop, we show that parameters are reduced from 4 to 2. The results presented here
will be useful in population viability analysis, population recovery planning, translocation planning,
and hunting and harvest management.
27
Mathematical Models of Community-acquired and Hospital-acquiredMethicillin-resistant Staphylococcus Aureus (MRSA) transmission
in Hospital and Community Settings
Wandi Ding
Middle Tennessee State University
Keywords: MRSA, optimal control, ODEs
Abstract: Optimal control methods are applied to two deterministic mathematical models to
investigate:
Model 1: To characterize the factors contributing to the replacement of hospital-acquired
methicillin-resistant Staphylococcus aureus (HA-MRSA) with community-acquired methicillin-re-
sistant Staphylococcus aureus (CA-MRSA), and quantify the effectiveness of three interventions
aimed at limiting the spread of CA-MRSA in healthcare settings. Characterizations of the optimal
control strategies are established, and numerical simulations are provided to illustrate the results.
Model 2: To investigate MRSA spread and control in a community setting.
28
From individual-based birth-death processes tomacro-evolutionary patterns
Michael Doebeli
University of British Columbia
Keywords: macroevolution, birth-death processes, adaptive dynamics, phylogeny, diversification
Abstract: Most macro-evolutionary models are based on processes that occur at the species level,
such as lineage splitting and extinction. Ecological interactions are rarely considered in such models,
even though it is generally acknowledged that they are important for macroevolutionary processes.
On the other hand, microevolutionary models that take ecological interactions into account, e.g. to
investigate diversification, are rarely extrapolated to macroevolutionary timescales. Here I report
on some attempts to bridge these gaps by constructing models for long-term evolutionary dynamics
based on individual-based ecological interactions. I show how the nature of the (co-)evolutionary
dynamics changes as diversity evolves in high-dimensional phenotype spaces, and I will describe
the phylogenetic trees that result in the long run from such diversification processes. Traditional
phylogenetic methods can be used to analyze these trees. This work contributes to a unification
of micro- and macro-evolutionary models and leads to new perspectives on the macro-evolutionary
patterns generated by microevolutionary processes.
29
Combining Models and Data to Understand the Mechanisms DrivingInsect Outbreaks
Greg Dwyer
Ecology & Evolution, U. Chicago
Keywords: Host-pathogen, population cycles, model selection, high-performance computing
Abstract: Many forest-defoliating insects undergo periodic outbreaks, in which their densities rise
from very low levels, to levels at which defoliation and tree death are widespread. The effects of
outbreaks would be far more severe if not for attacks by host-specific parasitoids and pathogens,
which can cause in excess of 99% mortality in high density forest defoliator populations. Simple
host-pathogen and host-parasitoid models produce population cycles with periods and amplitudes
that match those seen in outbreak cycles in nature, but other types of data suggest that the simplest
models neglect key mechanisms that play a role in population cycles in nature. A deeper under-
standing of these missing mechanisms, however, requires experiments that are expressly designed to
test models, as well as high-performance computing algorithms to choose between competing mod-
els using multiple data sets. Using this interdisciplinary approach, research in my lab has revealed
the key roles of insect-pathogen evolution, variation in insect host-tree quality, and global climate
change in driving insect outbreaks. Moreover, because of the economic importance of outbreaks in
determining the fate of forests, our work has direct applications in biological control.
30
Connecting models with data: identifiability and uncertaintyin modeling disease dynamics
Marisa C. Eisenberg
Departments of Epidemiology and Mathematics
University of Michigan, Ann Arbor
Keywords: identifiability, parameter estimation, cholera, infectious disease
Abstract: Connecting dynamic models with data to yield predictive results often requires a va-
riety of parameter estimation, identifiability, and uncertainty quantification techniques. These ap-
proaches can help to determine what is possible to estimate from a given model and data set, and
help guide new data collection. Here, we examine how parameter estimation and disease forecasting
are affected when examining disease transmission via multiple types or pathways of transmission.
Using examples taken from cholera outbreaks in Haiti and Thailand, as well as the West Africa
Ebola epidemic, we illustrate some of the potential difficulties in estimating the relative contribu-
tions of different transmission pathways, and show how alternative data collection may help resolve
this unidentifiability. We also illustrate how even in the presence of large uncertainties in the data
and model parameters, it may still be possible to successfully forecast the disease dynamics.
31
A Discrete Mathematical Model for the Aggregation of -Amyloid
Saber Elaydi
Trinity University
keywords: -Amyloid, monomers, oligomers, Alzheimer Disease
Abstract: Alzheimer’s disease (AD) is an age-related, progressive degenerative disorder charac-
terized by the loss of synapses and neurons from the brain. Monomers of -Amyloid aggregate to
form oligomers and oligomers aggregate to form fibrils. Our study is based on the assumption that
soluble -A oligomers are the causative agents of AD, due to their toxicity to neuron cells in the
brain.
We develop a five-dimensional discrete mathematical model for the aggregation of monomers
into oligomers. The model establishes a theoretical mechanism to reduce the production of oligomers.
We provide conditions for the stability of the aggregation of -Amyloid. We establish a formula for
the number of monomers required for the production of -A oligomers. A mechanism to prevent
monomers from aggregating to oligomers is proposed for practitioners in the field of Alzheimer
Disease. This provides health providers a method for the prevention of Alzheimer Disease.
References
[1] S Elaydi et al., The Role of Cholesterol in Stress Related Neuronal Death, Cogent (2017).
[2] S Elaydi et al., HT22 Plasma Membrane Cholesterol does not alter neuronal sensitivity to -
Amyloid, Submitted.
[3] J. Hardy and D.J. Selkoe, The amyloid hypothesis of Alzheimer’s disease: Progress and problems
on the road to therapeutics, Science 297 (2002): 353—356.
[4] I.K. Puri and L. Li, Mathematical modeling for the pathogensis of Alzheimer’s disease, PLOS
ONE 5 (2010): c15176.
[5] D.J. Selkoe and J. Hardy The Amyloid hypothesis of Alzheimer’s disease at 25 years, EMBO
Molecular Medicine 8 (2016): 595—608.
[6] K. Hasegawa, M. Yamach, H. Naiki, Kinetic modeling and determination of reaction constants
of Alzheimer’s beta amyloid fibril extension and dissociation using surface plasma resonance, Bio-
chemistry 41(2002):13489-98.
32
Prey-Predator-Parasite: An Ecosystem Model With Fragile Persistence
Alex P. Farrell
North Carolina State University
Keywords: differential equations, predator-prey, infection, host extinction, persistence, coexis-
tence, Chytridiomycosis
Abstract: Chytridiomycosis is an amphibian fungal disease which has led to the decline, and
possibly the disappearance, of frog species in the Americas and Australia. This has rekindled
interest in whether infectious diseases alone (without Allee effects or reservoirs, e.g.) have the
potential to drive their host species into extinction. Since predators are a natural part of ecosystems,
a model consisting of predator, prey, and parasite populations is analyzed. A variety of behaviors
emerge, including parasite mediated persistence of the predator, survival of the ecosystem at high
initial predator levels and ecosystem collapse at low initial predator levels, and persistence of all
three species, and more.
References
[1] Collins, J.P., Amphibian decline and extinction: What we know and what we need to learn, Dis.
Aquat. Org. 92 (2010): 93-99
33
Plant toxins and trophic cascades alter fire regime and successionon a boreal forest landscape
Zhilan Feng
Purdue University
Keywords: Differential equation models, Plant-herbivore interactions, functional response
Abstract: Earlier models of plant-herbivore interactions relied on forms of functional response
that related rates of ingestion by herbivores to mechanical or physical attributes such as bite
size and rate. These models fail to predict a growing number of findings that implicate chemical
toxins as important determinants of plant-herbivore dynamics. Specifically, considerable evidence
suggests that toxins set upper limits on food intake for many species of herbivorous vertebrates.
Herbivores feeding on toxin-containing plants must avoid saturating their detoxification systems,
which often occurs before ingestion rates are limited by mechanical handling of food items. We
developed mathematical models with toxin-determined functional responses to study the effects
of inter-specific plant competition, herbivory, and a plant’s toxic defenses against herbivores on
vegetation dynamics. The new models exhibit much more complex dynamics including Hopf and
homoclinic bifurcations. We used the model to estimate the effects of different levels of wolf
control. Simulations indicated that management reductions in wolf densities could reduce the mean
time to transition from deciduous to spruce by more than 10 years, thereby increasing landscape
flammability. The integrated model can be useful in estimating ecosystem impacts of wolf control
and moose harvesting in central Alaska.
References
[1] Feng, Z., DeAngelis, D. L., Mathematical Models of Plant-Herbivore Interactions, CRC Press,
Taylor & Francis Group, 2017
[2] Feng, Z., Alfaro-Murillo, J. A., DeAngelis, D. L., Schmidt, J., Barga, M., Zheng, Y., Ahmad
Tamrin, M.H.B., Olson, M., Glaser, T., Kielland, K., Chapin III, F. S., Bryant, J., Plant toxins and
trophic cascades alter fire regime and succession on a boreal forest landscape, Ecological Modeling
244 (1012): 79-92
[3] Castillo-Chavez C., Feng, Z., Huang, W., Global dynamics of a plant-herbivore model with
toxin-determined functional response, SIAM J. Appl. Math. 72 (2012): 1002-1020
[4] Feng Z., Qiu Z., Liu, R., DeAngelis, D. L., Dynamics of a plant-herbivore-predator system with
plant-toxicity, Math. Biosci., 299 (2-11): 190-204
[5] Feng, Z., Liu, R. and DeAngelis, D. L., Bryant, J. P., Kielland, K., Chapin, F. S. III, Swihart,
R. K., Plant toxicity, adaptive herbivory, and plant community dynamics, Ecosystems, 12 (2009):
534-547
[6] Liu, R., Feng, Z., Zhu, H. and DeAngelis, D. L., Bifurcation analysis of a plant-herbivore model
with toxin-determined functional response, J. Differential Equations, 245 (2008): 442-467
[7] Feng, Z., Liu, R. and DeAngelis, D. L., Plant-herbivore interactions mediated by plant toxicity,
Theor. Pop. Biol. 73 (2008): 449-459
34
A game-theoretic approach to modeling ecological dynamics
Theodore E. Galanthay
Ithaca College
Keywords: game theory, foraging dynamics, aggression, Hawk-Dove model
Abstract: The Hawk-Dove game theoretic model attempts to explain the evolution of aggression
between animals. This model has two parameters that represent Reward and Cost. Recent work
[1] introduced theory to incorporate interaction times into two-player matrix games. We apply that
theory to develop a series of models to connect the classical Hawk-Dove model to more mechanistic
ecological models. We use these models to study the evolution of aggression.
References
[1] Krivan, V. and Cressman, R., Interaction times change evolutionary outcomes: Two player
matrix games, Journal of Theoretical Biology (2017): 199-207
35
Using Homogenization to Estimate Random-Walk Motility fromTelemetry Data in Heterogeneous Landscapes
Martha Garlick
South Dakota School of Mines and Technology
Keywords: ecological diffusion, resource selection functions, parameter estimation
Abstract: The availability of land classification data sets and GPS location data has greatly
impacted ecological studies. However, incorporating this data into meaningful spatial models can
be challenging. Ecological diffusion models connect animal movement to heterogeneous landscapes
through motility parameters (constants with units of area/time). Combining ideas from resource
selection analysis and a homogenization technique for ecological diffusion, we devise a way to
estimate motilities from land cover and GPS location data. Motilities can then be incorporated into
spatial models dealing with invasive spread, spread of disease, habitat use or population dynamics.
36
How the distribution for the time since infection to recovery affectsthe course of an epidemic
Li Guan
Department of Mathematics, Tulane University
Keywords: epidemic model, ordinary differential equation, generalized distribution model
Abstract: Most mathematical models assume that the rate people recover from an infection is
independent of the length of time they have been infected. This assumption leads to an exponen-
tially distributed waiting time from infection to recovery that can be a poor approximation of the
actual recovery distribution. We use theoretical analysis and numerical simulations to demonstrate
how the solution of susceptible-infected-recovery (SIR) epidemic models depends on this assump-
tion by comparing different distributions for the time from infection to recovery. We also analyze
how the assumed distribution for the time from infection to recovery affects the estimates for the
reproductive number and model parameters based on epidemic infection data.
This research was in collaboration with Nick Hengartner (Los Alamos National Laboratory)
and Mac Hyman (Tulane University)
37
Modeling Distinct Virus Infection Strategies in Virus-Microbe Systems
Hayriye Gulbudak
Department of Mathematics, University of Louisiana at Lafayette
Abstract: Viruses of microbes, including bacterial viruses (phage), archaeal viruses, and eukaryotic
viruses, can influence the fate of individual microbes and entire populations. Here, we model distinct
modes of virus-host interactions and study their impact on the abundance and diversity of both
viruses and their microbial hosts. We consider two distinct viral populations infecting the same
microbial population via two different strategies: lytic and chronic. A lytic strategy corresponds
to viruses that exclusively infect and lyse their hosts to release new virions. A chronic strategy
corresponds to viruses that infect hosts and then continually release new viruses via a budding
process without cell lysis. The chronic virus can also be passed on to daughter cells during cell
division. The long-term association of virus and microbe in the chronic mode drives differences in
selective pressures with respect to the lytic mode. We utilize invasion analysis of the corresponding
nonlinear differential equation model to study the ecology and evolution of heterogenous viral
strategies. We first investigate stability of equilibria, and characterize oscillatory and bistable
dynamics in some parameter regions. Then, we derive fitness quantities for both virus types and
investigate conditions for competitive exclusion and coexistence. In so doing we find unexpected
results, including a regime in which the chronic virus requires the lytic virus for survival and
invasion.
38
Effect of temperature on the dynamics of malaria vector and disease:a theoretical analysis
Abba B. Gumel
School of Mathematical and Statistical Sciences, Arizona State University (ASU)
Keywords: malaria, temperature, equilibria, stability
Abstract: The talk focuses on the design, analysis and simulation of a new model for assessing
the impact of temperature on the population biology of the malaria vector (Anopheles mosquito)
and malaria disease in a community. Some of the novel features of the model include the detailed
lifecycle of the vector, the vector’s gonotrophic cycle as well as the sporogony of the malaria
parasite. Suitable temperature ranges for maximum mosquito abundance (hence, maximum disease
incidence) will be derived. If time permits, global malaria maps will be generated by simulating the
model under various climate change projections. This is a collaborative work with S. Eikenberry
and K. Okuneye of ASU.
References
[1] Kamaldeen Okuneye, Ahmed Abdelrazec and Abba Gumel. Mathematical analysis of a weather-
driven model for population ecology of mosquitoes. Mathematical Biosciences and Engineering.
15(1)(2018): 57-93.
[2] Ahmed Abdelrazec and Abba B. Gumel. Mathematical assessment of the role of temperature and
rainfall on mosquito population dynamics. Journal of Mathematical Biology. 74(2017): 13511395.
[3] Kamaldeen Okuneye and Abba B. Gumel. Analysis of a temperature- and rainfall-dependent
model for malaria transmission dynamics. Mathematical Biosciences. 287(2017) 7292.
[4] F. Agusto, A.B. Gumel and P.E. Parham. Qualitative assessment of the role of temperature
variations on malaria transmission dynamics. Journal of Biological Systems. 23(4)(2015): 1-34.
[5] Steffen Eikenberry and Abba Gumel. Mathematics of climate change and malaria transmission
dynamics. Submitted (review paper).
[6] A temperature- and rainfall-dependent malaria vector model incorporating microhabitat hydro-
dynamics, nutrient-limited growth, and age-dependent survival. Submitted.
39
Temperature-dependent Model for the Dynamics of Zoonotic VisceralLeishmaniasis
in Human and Animal Reservoir Populations
N. Hussaini
Bayero University Kano, P.M.B. 3011, Kano, Nigeria.
Keywords: Leishmania infantum, autonomous and non-autonomous models, stability, sensitivity
and uncertainty analyses.
Abstract: Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania
infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many
parts of the world (notably Africa, Asia and the Mediterranean). This study presents a new
mathematical model for assessing the impact of seasonal variations in temperature on the trans-
mission dynamics of ZVL in human and sylvatic animal reservoir populations. Both autonomous
and non-autonomous versions of the model have been rigorously analysed. Finally, sensitivity and
uncertainty analyses, using data relevant to ZVL dynamics in Amhara, Ethiopia and Bihar, India,
have been performed.
40
Dynamics of a population in two patches with dispersal
Sophia Jang
Department of Mathematics and Statistics, Texas Tech University
Abstract: A two-dimensional discrete system of a species in two patches proposed by Newman et
al. is studied. It is shown that the unique interior steady state is globally asymptotically stable
if the active population has a Beverton-Holt type growth rate. If the population is also subject
to Allee effects, then the system has two interior steady states whenever the density-independent
growth rate is large. In addition, the model has period-two solutions if the symmetric dispersal
exceeds a critical threshold. For small dispersal, populations may either go extinct or eventually
stabilize. However, populations are oscillating over time if dispersal is beyond the critical value
and the initial populations are large.
41
Dynamics of Hierarchy Establishment from Nonlinear SocialInteractions and Metabolic Costs
Yun Kang
Arizona State University
Keywords: Hierarchy, Social Interactions, Reproduction Ratio, Metabolic Theory
Abstract: After the queen dies, the ant species H. saltator colony forms a new hierarchy group
called gamergates (about 15-20% of the colony size) who replace the reproducing function of the
queen. Motived by this, we develop and study a general mechanistic population model based on
nonlinear social interactions and ecology metabolism theory to explore how life history parameters
and the related metabolic costs shape the hierarchy structure of social groups including ant colonies.
More specifically, we aim to use the model combined with the experimental data to address:
1. What are the key life history parameters that determine the colony size?
2. How do the metabolic parameters affect the colony size and the reproductive class?
3. How do the colony size and the size of the reproductive class regulate each other?
42
Rich Dynamics of a Stoichiometric Food Chain Modelwith Two Limiting Nutrients
Yang Kuang
Arizona State University
Keywords: stoichiometry, predator-prey system, food quality, C:P ratio
Abstract: Ecological stoichiometry studies the balance of energy and multiple chemical elements in
ecological interactions to establish how the nutrient content affect food-web dynamics and nutrient
cycling in ecosystems. Stoichiometric population models aim to describe fully the complex dynamics
often observed in nature in a simple and sound setting. In this study, we formulate a food chain
with two limiting nutrients in the form of a stoichiometric population model. This model naturally
extends the LKE model due to Loladze, Kuang and Elser. A comprehensive global analysis of the
rich dynamics of the targeted model is explored both analytically and numerically. Chaotic dynamic
is observed in this simple stoichiometric food chain model and is compared with traditional model
without stoichiometry. Our finding shows that decreasing producer production efficiency may have
only a small effect on the consumer growth but a more profound impact on the top predator growth.
References
[1] M. Chen, M. Fan, and Y. Kuang, Global dynamics in a stoichiometric food chain model with
two limiting nutrients, Mathematical Biosciences 289 (2017): 9-19.
[2] X. Yang, X. Li, H. Wang, and Y. Kuang, Stability and bifurcation in a stoichiometric producer-
grazer model with knife edge, SIAM J. on Applied Dynamical Systems 15 (2016): 2051-2077.
43
Three paradoxical results for ecosystem management by multiple agents
Adam Lampert
School of Human Evolution and Social Change,
and
Mathematical, Computational and Modeling Science Center,
Arizona State University, AZ 85281
Keywords: Ecosystem Management, Harmful Species, Dynamic Games
Abstract: A major threat to human well-being is the accelerated rate of ecosystem degradation.
Restoration of degraded ecosystems, including harmful species control, entails cooperation among
multiple agents such as land-owners, agencies and sometimes countries. These agents may have
incentives to contribute less, leaving the job for other agents (free-ride), which may lead to inefficient
or incomplete treatment. Ecosystem restoration is a dynamical process that may span over many
years, particularly due to life histories of both harmful and native species. A major question is what
factors facilitate or impede long-term cooperation among agents. I will introduce a dynamic game
approach to study how to restore ecosystems by multiple agents, taking into account the costs of
both treatment and degradation over time. We assume no enforcement mechanisms and no binding
agreements (namely, each agent cooperates only for its selfish interests). In my talk, I will show
that, under certain conditions, there exists a solution (Markovian Nash equilibrium) where all agents
contribute, albeit slowly enough, and no agent has an incentive to further free-ride. Nevertheless,
there are several factors that affect the efficiency or the solution, some of which are counterintuitive
and seem paradoxical. First, agents with fewer incentives to contribute, such as agents that are less
affected by the harmful species, may nonetheless contribute more than the others at equilibrium.
Second, monitoring agents’ actions (to know how much each agent really contributes) may impede
cooperation and incentivize less contribution. Third, incomplete information about agents’ true
objectives may increase cooperation. Our results emphasize the importance of further using game
theory to study how to manage ecosystems by multiple agents.
44
A Mathematical Model for Onchocerciasiswith Intermittent Treatment
Glenn Ledder
University of Nebraska-Lincoln
Keywords: epidemiology, vector-borne disease, nonlinear incidence, periodic dynamical system
Abstract: Onchocerciasis is an endemic disease in parts of sub-Saharan Africa. Complex mathe-
matical models are being used to assess the likely efficacy of efforts to eradicate the disease; however,
their predictions have not always been borne out in practice. For a simpler model, we represent
the immunological aspects of the disease by a single empirical parameter and use asymptotic ap-
proximation to reduce the vector-borne epidemiological model to a model of an infectious disease
with nonlinear incidence. We consider a version with continuous treatment and a more realistic
one where treatment occurs only at intervals. Thorough mathematical analysis of these models
yields equilibrium solutions for the continuous case, periodic solutions for the pulsed case, and
conditions for the existence of endemic disease equilibria in both cases, thereby leading to simple
model criteria for eradication. The analytical results and numerical experiments show that the
continuous treatment version is an excellent approximation for the pulsed version and that the
current onchocerciasis eradication strategy is inadequate for regions where the incidence is highest
and unacceptably slow even when the long-term behavior is the disease-free state.
45
Genetic consequences of range expansion under climate change
Mark Lewis
Department of Biological Sciences and the Department of Mathematical and Statistical Sciences,
University of Alberta, Edmonton T6G2G1, Canada
Abstract: Range expansion is a crucial population response to climate change. Genetic conse-
quences are coupled to ecological dynamics that, in turn, are driven by shifting climate conditions.
We model a population with a reaction-diffusion system, coupled to a heterogeneous environment
that shifts with time due to climate change. We decompose the resulting traveling wave solution
into neutral genetic components to analyze the spatio-temporal dynamics of its genetic structure.
Our analysis shows that range expansion under slow climate change preserves genetic diversity.
However, diversity is diminished when climate change occurs too quickly. We show that popula-
tions with intermediate dispersal ability are best for maintaining genetic diversity. Our study also
provides new insight regarding traveling wave solutions in heterogeneous environments. We show
how related results can be derived in the context of integro-difference equations. This is joint with
Jimmy Garnier (CNRS), Zhongwei Shen (Alberta) and Nathan Marculis (Alberta).
46
Complex Spatial Dynamics in Integro-Difference Equations
Bingtuan Li
University of Louisville
Keywords: integro-difference equation, Allee effect, spreading speed
Abstract: It is well-known that density dependence generates temporal fluctuations in population
density. However, the ways in which density dependence affects spatial population processes, such
as species invasions, is less understood. In this talk, we show that in integro-difference equations,
density dependence in demography at low population densities - i.e., an Allee effect - combined with
overcompensatory population growth can produce fluctuations in spreading speed and solutions that
do not expand their spatial ranges. Our results demonstrate that simple rules can generate complex
spatial dynamics, and highlight a novel source of variability in biological invasions that may aid in
ecological forecasting. (Joint work with Lauren L. Sullivan, Tom E. X. Miller, Michael G. Neubert,
Allison K. Shaw, and Garrett Otto.)
References
[1] L. L. Sullivan, B. Li, T. E. X. Miller, M. G. Neubert, and A. K. Shaw, Density dependence
in demography and dispersal generates fluctuating invasion speeds, Proceedings of the National
Academy of Sciences 114 (2017), 5053-5058.
47
Discrete-time Structured Model for Malaria Transmissionwith constant releasing sterile mosquitoes
Yang Li
University of Louisiana at Lafayette
Keywords: Malaria transmission, discrete-time, sterile mosquitoes, constant release, numerical
simulations
Abstract: To incorporate the interactive mosquitoes into malaria transmissions, we formulate
susceptible-exposed-infective-recovered (SEIR) compartmental discrete-time models, which are of
high dimensions, and then include the interactive mosquito models into these disease models. We
derive formulas for the reproductive number 0 of infection for the malaria models with or without
sterile mosquitoes and explore the existence of endemic fixed points as well. We then study the
impact of sterile mosquitoes releases on the disease transmissions by investigating the effects of
varying the releases of sterile mosquitoes. We use numerical simulations to verify our results for all
cases and finally give brief discussions of our findings and future study.
References
[1] L.Allen and P. van den Driessche, The basic reproduction number in some discrete-time epidemic
models, J.Difference Equ. Appl. 14 (2008), 1127 - 1147.
[2] R. M. Anderson and R. M. May, Infectious Disease of Humans, Dynamics and Control, Oxford
University Press, 1991.
[3] C.Castillo-Chavez and A. Yakubu, Discrete-time S-I-S models with complex dynamics, Nonlinear
Anal. 47 (2001), 4753 - 4762.
[4] J.M.Cushing and Z.Yicang, The net reproductive value and stability in matrix population models,
Nat. Res. Model. 8 (1994), 297 - 333.
[5] J. Li, Malaria models with partial immunity in humans, Math. Biol. Eng 5(2008), 789 - 801.
[6] G.A.Ngwa, Modeling the dynamics of endemic malaria in growing populations, Discrete Contin.
Dyn. Syst. Ser B 4 (2004), 1172 - 1204.
[7] G.A.Ngwa, On the population dynamics of the malaria vector, Bull. Math. Biol. 68 (2006),
2161 - 2189.
48
Adaptive desynchronization and synchronizationin coupled biological oscillators
Wei Lin
School of Mathematical Sciences and Institute of Science and Technology for Brain-Inspired
Intelligence
Fudan University, Shanghai 200433, China
Abstract: In this talk, we will present several adaptive control protocols, including feedback
control with time delay and feedback control set in a merely stochastic version. We will validate
the feasibility of our proposed protocols, not only for a large population of coupled oscillators, but
also for representative neuronal network models. We also will present several factors of physical
or biological significance essential to the success of our proposed protocols. We anticipate that
our protocols will deepen the understanding and refinement of those controllers, e.g. techniques of
deep brain stimulation, which have been implemented in remedying some synchronization-induced
mental disorders including Parkinson disease and epilepsy.
References
[1] Shijie Zhou, Peng Ji, Qing Zhou, Jianfeng Feng, Jürgen Kurths, and Wei Lin, Adaptive elimi-
nation of synchronization in coupled oscillator, New Journal of Physics (2017) vol. 19, Article no.
083004.
[2] Wei Lin, Xin Chen, and Shijie Zhou, Achieving control and synchronization merely through a
stochastically adaptive feedback coupling, CHAOS (2017) vol. 27, Article no. 073110.
49
How predator behavior and seasonality affect predator-prey dynamics
Frithjof Lutscher
Department of Mathematics and Statistics, University of Ottawa
Keywords: predator-prey dynamics, functional response, behavior switch, climate change
Abstract: The population cycles of lynx and snowshoe hare in Western Canada are among the
best-known examples for cyclic dynamics in predator-prey communities, and many other examples
exist. Decades of empirical and theoretical research demonstrate that predation by specialists can
destabilize a community and lead to sustained population cycles, whereas predation by generalists
is typically thought to stabilize a coexistence equilibrium. Detailed data from the Kluane project
suggest that a predator may change its behaviour from specialist to generalist seasonally. More
specifically, the great horned owl preys on snowshoe hares as a generalist predator during the
summer, but as a specialist during the winter. Several other examples of such seasonal behaviour
shifts exist. What then are the effects of such behaviour shifts on the dynamics of predator and
prey? And how could expected effects of global change alter the dynamics of these systems? In this
talk, I will present a minimal mathematical model to address these questions and illustrate some
of the dynamics that result. In particular, I will demonstrate that generalist predation may lead
to population cycles; that seasonal behaviour changes of the predator might lead to extinction of
the prey; that predators may benefit more than prey from longer summer seasons; and that cyclic
dynamics can appear or disappear suddenly.
References
[1] R. Tyson and F. Lutscher, Seasonally Varying Predation Behavior and Climate Shifts Are
Predicted to Affect Predator-Prey Cycles, The American Naturalist 188(5) (2016): 539—553
50
How does within-host dynamics affect population-level dynamics?Insights from an immuno-epidemiological model of malaria
Maia Martcheva
University of Florida
Keywords: age since infection, basic reproduction number, global stability, immuno-epidemiology,
Lyapunov functional, malaria, oscillations, vector-host model
Abstract: Malaria is one of the most common mosquito-borne diseases widespread in the trop-
ical and subtropical regions. Few models coupling the within-host malaria dynamics with the
between-host mosquito-human dynamics have been developed. In this talk, by adopting the nested
approach, a malaria transmission model with immune response of the host will be introduced.
Applying age-structured partial differential equations for the between-host dynamics, we describe
the asymptomatic and symptomatic infectious host population for malaria transmission. The ba-
sic reproduction numbers for the within-host model and for the coupled system are derived. The
existence and stability of the equilibria of the coupled model are analyzed. We show numerically
that the within-host model can exhibit complex dynamical behavior, possibly even chaos. In con-
trast, equilibria in the immuno-epidemiological model are globally stable and their stabilities are
determined by the reproduction number. Increasing the activation rate of the within-host immune
response “dampens” the sensitivity of the population level reproduction number and prevalence to
the increase of the within-host reproduction of the pathogen. From public health perspective this
means that treatment in a population with higher immunity has less impact on the population-level
reproduction number and prevalence than in a population with less immunity.
51
Methods for Parameter Estimation of a StochasticSEIR Model using Bayesian Inference
Kaitlyn Martinez
Colorado School of Mines
Keywords: Epidemiology, SEIR model, Approximate Bayesian Computation, Ordinary Differen-
tial Equations
Abstract: This project aims to extend the framework of stochastic analysis epidemic models that
are derived from a set of ordinary differential equations (ODEs) and are based on the underlying
biological and spatial spread of disease. By implementing Bayesian Inference, this project proposes
novel parameterizations of infectious disease models in the susceptible, exposed, infectious, removed
(SEIR) class, and explores various methods to estimate these parameters. Approximate Bayesian
Computation (ABC) is used for estimating population distributions and the model parameters.
ABC uses a batch of proposed parameters to generate simulated data that can be assess as “close
to” or “far from” the real data under some norm. Historically, these methods are limited from
extension to spatial models, as many SEIR models consider infectious counts, rather than propor-
tions of people relative to the total population. Thus, there are considerable modeling challenges
that must be assessed in conjunction with these computational difficulties to develop viable spatial
models. The final stage of this project aims to develop ABC methods that can propose parame-
ters and generate populations using proportions. This will allows us to extend the framework to
stochastically analyze systems of PDEs, which is novel in the spatial epidemic literature.
52
Individuals are discrete and it matters: an example using the lottery model
Joanna Masel
Department of Ecology and Evolutionary Biology, University of Arizona
Abstract: Populations are made of up discrete individuals. It is often mathematically convenient
to treat abundances as approximately continuous (infinite population size approximation), but this
can lead to absurd outcomes even for very large populations. Here we give an example of how
properly accounting for the behavior of rare types can dramatically alter the dynamics of a large
population by relaxing the infinite population size assumption in the lottery model, generalizing
it to arbitrary densities. The lottery model is used in ecology to describe population dynamics
in the presence of territorial contests, and is closely connected to the Wright-Fisher model of
population genetics. We show once the behavior of rare types is handled correctly, co-existence
becomes possible in a stable environment; behavior that is eliminated in the infinite population size
approximation. The discreteness of individuals is essential to understanding the behavior of rare
types.
References
[1] J. Bertram, J. Masel, A lottery model of density-dependent selection in evolutionary genetics,
2017 (preprint https://doi.org/10.1101/102087)
53
Population Dynamics of the Honeybee-mite Interactions
Komi Messan
Simon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State
University, Tempe, AZ 85281, USA
Keywords: migration, honeybee, mite, colony loss, extinction
Abstract: Honeybees are amazing and highly beneficial insect species that play important roles
in our ecosystem and agriculture. Unfortunately, honeybees are increasingly threatened by an
onslaught of harmful influences, especially the parasitic Varroa mites. A recent field study in
[1] shows that migrations of mites through their attachment to forager bees contribute greatly
to the rapid growth of mite population, and increase the mortality of honeybee colonies that
could eventually cause their collapsing. Motivated by this, we first propose a simple two-patch
honeybee-Varroa model to explore how foraging behavior of honeybees in the presence of Varroa
mite infestations affect the population dynamics of honeybees and mites, respectively. We then
provide another single patch model to study the effect of brood infestation on the population
dynamics of both adult honeybee and brood. Our analytical and numerical studies reveal the
dynamical outcomes of migration including the destabilization and stabilization effect of brood
infestation. Our results provide novel insights on the effects of foraging and Varroa mites on colony
survival.
References
[1] DeGrandi-Hoffman, G., Ahumada, F., Zazueta, V., Chambers, M., Hidalgo, G., and Watkins
deJong, E., Population growth of varroa destructor (acari: Varroidae) in honey bee colonies is
affected by the number of foragers with mites, Experimental and Applied Acarology, (2016) 69(1):21-
34.
54
Spatial models of population dynamics and quantitative traits
Judith R. Miller
Georgetown University
Keywords: Biological invasions, local adaptation, range pinning, reaction-diffusion equations,
patchy habitat, traveling waves
Abstract: We model the joint evolution of a population density and the mean, and sometimes
variance, of a quantitative trait subject to stabilizing selection toward an optimum that varies in
space. To do so, we study a family of deterministic models originating from the Kirkpatrick-Barton
(1997) reaction-diffusion system. We use analysis and numerics to identify conditions under which
the models predict range pinning due to an influx of locally maladapted individuals from the center
of a species’ range to its borders (“genetic swamping”) versus invasions represented as travelling
waves. We highlight differences between the predictions of the Kirkpatrick-Barton model and those
of related models incorporating features, such as non-Gaussian dispersal kernels and patchy habitat,
that are often represented in nongenetic invasion models.
References
[1] M. Kirkpatrick and N. Barton, Evolution of a species’ range, Am. Nat. 150 (1997): 1—23.
55
A Technique to Approximate Hitting Probabilitieswith Applications to Metapopulation Models
Evan Milliken
Arizona State University, Tempe, AZ,
School of Mathematical and Statistical Sciences
Keywords: metapopulation, Markov chain, extinction
Abstract: At the instant an infectious individual is introduced to a susceptible population, the
low number of infectious individuals indicates the need for mathematical models that take random
fluctuations into account. In the case of Markov chain models, one commonly studied statistic is
the probability of disease extinction. Mathematically, this statistic is a hitting probability. In this
talk, a new technique for approximating hitting probabilities, called Local Approximation in Time
and Space (LATS) is introduced. LATS is shown to be universally applicable to hitting problems
with respect to Markov chains. When multiple smaller populations interact with each other to
form a population of populations, it is called a metapopulation. In the context of metapopulation
models, other interesting statistics, such as probability of partial extinction, can be formulated as
hitting probabilities. Specifically, LATS can be used to approximate the probability of extinction
in a single patch. This probability is utilized to measure the degree to which a patch is at risk of
outbreak. It is also used to assess the efficacy of heterogenous control strategies.
56
Structured population model with diffusion in structure space
Fabio A. Milner
School of Mathematical and Statistical Sciences
Arizona State University
P.O. Box 871804
Tempe, AZ 85287-1804
Keywords: diffusion model, structured-population, stochastic individual dynamics
Abstract: A structured population model is described and analyzed, in which individual dynamics
may be stochastic. The model consists of a PDE of advection-diffusion type in the structure
variable. The population may represent, for example, the density of infected individuals structured
by pathogen density ≥ 0. The individuals with density = 0 are not infected, but rather
susceptible or recovered. Their dynamics is described by an ODE with a source term that is the
exact flux from the diffusion and advection as → 0+. Infection/reinfection is then modeled
by distributing some fraction of these individuals into the infected class, but distributed in the
structure variable through a probability density function. Existence of a global-in-time solution
is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction
number R0 is defined that separates the case of only the trivial equilibrium existing when R0 1from the existence of another –notrivial– equilibrium when R0 1. Numerical simulation resultsare provided to show the stabilization towards the positive equilibrium when R0 1 and towardsthe trivial one when R0 1, result that is not proven analytically. Simulations are also provided
to show the Allee effect that helps boost population sizes at low densities.
57
Acquired metabolism as an evolutionary path to mixotrophy
Holly V. Moeller*
Department of Ecology, Evolution & Marine Biology
University of California, Santa Barbara
and
Michael G. Neubert
Biology Department
Woods Hole Oceanographic Institution
Keywords: adaptive dynamics, evolutionary ecology, intraguild predation, omnivory
Abstract: Acquired metabolism–metabolism that is not encoded within an organism’s genome,
but which is instead obtained through interactions with other species–mediates species interac-
tions that shape both community composition and function. One example of this is acquired
phototrophy, the acquisition of photosynthetic abilities through the retention of prey chloroplasts
or hosting of photosynthetic endosymbionts. Unicellular, planktonic acquired phototrophs range
in the degree to which they rely on their acquired metabolism. Most are mixotrophic, combining
photosynthesis and heterotrophy to meet the energetic and material demands of growth and re-
production. Acquisitions also provide opportunity for evolutionary innovation because they allow
organisms to access metabolic pathways completely novel to their evolutionary lineage. We de-
veloped mathematical models for acquired metabolism grounded in experimental data, and used
adaptive dynamics to study how organisms evolve from strict predators to mixotrophs through
two key transitions: First, the ability to retain metabolic machinery from their prey, and second,
the ability to replicate this machinery (thereby permanently incorporating it into the organism’s
metabolic repertoire). Our approach illustrates how acquired metabolism may allow new lineages
to emerge from a background of closely related competitors, ultimately providing insight into the
evolution of the modern eukaryotic phytoplankton.
58
A model of natural selection predicts treatment resistancein prostate cancer
John D. Nagy
Department of Life Sciences, Scottsdale Community College
School of Mathematical and Statistical Sciences, Arizona State University
Keywords: Cancer treatment, Data fitting, Mathematical oncology
Abstract: Standard of care treatment for recurrent and advanced prostate cancer includes chemi-
cal castration. Inevitably, however, such treatment results in hormone-refractory tumors with dire
prognosis. Clearly, a predictive mathematical model of this process would greatly improve our un-
derstanding and ability to mitigate castration resistance in this tumor. Here I develop an adaptive
dynamics model of androgen-ablation therapy and show that it predicts progression of treatment
resistance in a significant subset of prostate cancer patients. The model assumes that castration
resistance evolves due to natural selection on androgen receptor (AR) expression. Formulation
and parameterization of the model was completed based on a sample of 25 patients treated with
intermittent androgen ablation therapy. The model was then used to predict PSA dynamics in
an independent set of 30 patients from the same clinical study. Predictions were reasonably accu-
rate typically for one cycle, and for some patients up to 4 cycles. However, there were significant
exceptions–in some cases the model exhibited no predictive power. These observations are consis-
tent with the conclusion that the model accurately reflects castration resistance arising via natural
selection acting on AR expression, but fails for cases in which resistance is caused by a different
mechanism, like “outlaw” or AR bypass pathways. This modeling approach therefore may provide
a noninvasive method to identify emerging resistance mechanisms in nascent hormone-refractory
tumors and to plan treatment to delay development of castration resistance.
59
Somatic evolution and aging in multicellular organisms
Paul Nelson
Department of Ecology and Evolutionary Biology, University of Arizona
Abstract: Current theories attribute aging to a failure of selection, either due to pleiotropic con-
straints, or due to declining strength of selection after the onset of reproduction. These theories
implicitly leave open the possibility that, if senescence-causing alleles could be identified, or if
antagonistic pleiotropy could be broken, the effects of aging might be ameliorated or delayed indef-
initely. These theories are built on models of germline selection between multicellular organisms,
but a full understanding of aging also requires examining the role of somatic selection within an
organism. Selection between somatic cells, i.e. intercellular competition, can delay aging by purg-
ing non-functioning cells. But the fitness of a multicellular organism depends not just on how
functional its individual cells are, but also on how well cells work together. While intercellular
competition weeds out non-functional cells, it may also select for cells that do not cooperate. We
present a mathematical model of somatic evolution to show that intercellular competition creates
an inescapable double bind that makes aging inevitable in multicellular organisms.
60
Climate change and the bloom dynamics of a coastal phytoplankter
Michael Neubert*, Kristen Hunter-Cevera, and Heidi Sosik
Woods Hole Oceanographic Institution
Keywords: Phytoplankton Dynamics, Size Structure, Climate Change, Matrix Models
Abstract: Climate affects the timing and magnitude of phytoplankton blooms that fuel marine
food webs and influence global biogeochemical cycles. Changes in bloom timing have been de-
tected in some cases, but the underlying mechanisms remain elusive, contributing to uncertainty
in long-term predictions of climate change impacts. Understanding changes in phytoplankton cell
abundance requires estimates of division rates. These rates are difficult to obtain at the necessary
time scales (daily) for extended periods with conventional methods. We have shown that a matrix
population model [1], combined with observed hourly cell size distributions accurately estimates
division rates of both cultured and natural populations of the picocyanobacteria Synechococcus
[2]. In a 13-year, hourly time series of Synechococcus size spectra and abundance from the New
England shelf, the timing of the spring bloom varied by 4 weeks. We have shown that multiyear
trends are due to temperature-induced changes in cell division rate, with earlier blooms driven by
warmer spring water temperatures [3]. Synechococcus loss rates shift in tandem with division rates,
suggesting a balance between growth and loss that has persisted despite phenological shifts and
environmental change.
References
[1] H. M. Sosik, R. J. Olson, M. G. Neubert, A. Shalpyonok, Growth rates of coastal phytoplankton
from time-series measurements with a submersible flow cytometer, Limnology and Oceanography
48 (2003): 1756-1765.
[2] K. R. Hunter-Cevera, M. G. Neubert, A. R. Solow, R. J. Olson, A. Shalapyonok, H. M. Sosik,
Diel size distributions reveal seasonal growth dynamics of a coastal phytoplankter, Proceedings of
the National Academy of Science of the USA 111 (2014): 98529857.
[3] K. R. Hunter-Cevera, M. G. Neubert, R. J. Olson, A. R. Solow, A. Shalapyonok, H. M. Sosik,
Physiological and ecological drivers of early spring blooms of a coastal phytoplankter, Science 354
(2016): 326-329.
61
Evolution and Regulation of Syntrophic Symbiosis
Roger M Nisbet
University of California, Santa Barbara
Abstract: Dynamic Energy Budget (DEB) theory offers a natural framework for modeling mu-
tualistic interactions [1]. This was demonstrated in a model of coral, a “superorganism” whose
growth involves interactions between a heterotrophic host and a photoautotroph [2]. Balanced
growth, defined as growth with a stable ratio of host to symbiont biomasses, does not require
inter-organism communication (global control), but is an emergent property provided each species
makes available to its partner any surplus resource. I report on work in a NIMBioS working group
that has extended this formalism to interactions among organs (root and shoot) in a terrestrial
plant. The talk will describe a family of idealized models of interacting partners (organisms or
organs) with carbon and nitrogen dynamics that include “sharing the surplus”. We characterize
biosynthesis using two synthesizing unit (SU) representations: Liebig’s minimum rule (MRSU) and
the Parallel Complementary SU (PCSU) widely used in DEB applications [1]. With the MRSU,
stable balanced growth is achieved if at least one player needs a higher proportion than its partner
of the element that it cannot obtain directly. The asymptotic balanced growth rate is equal to that
previously shown using life history theory to be “optimal” for allocation of photosynthate between
roots and shoots in a growing plant [3]. During balanced growth, there is no unutilized carbon
or nitrogen. When the condition for balanced growth is violated, growth dynamics are oscillatory,
there is “wastage” of carbon and nitrogen, and the long run population growth rate is less than
could be achieved with global control. With biosynthesis represented with the PCSU, oscillatory
dynamics only occurs with extreme parameter values, but the rate of balanced growth is still opti-
mal in the sense that no reallocation of elements by some global (e.g. hormonal) controller increases
the growth rate. Adding additional feedbacks to the models may eventually cause breakdown of
balanced growth. This is demonstrated with a model of coral bleaching that exhibits bistability
and hysteresis, with balanced growth at both positive and negative rates being possible in the same
environment. In summary, our findings demonstrate that “sharing the surplus” leads to robust,
evolutionarily plausible, dynamics, that may, nonetheless, be sensitive to environmental change.
References
[1] Kooijman, S. A. L. M. 2010. Dynamic Energy Budget Theory for Metabolic Organization.
Cambridge University Press, Cambridge, UK.
[2] Muller, E. B., S. A. L. M. Kooijman, P. J. Edmunds, F. J. Doyle, and R. M. Nisbet. 2009.
Journal of Theoretical Biology 259:44-57.
[3] Velten, K., and O. Richter. 1995. Bulletin of Mathematical Biology 57:99-107.
62
The complex dynamics of a diffusive prey-predator modelwith an Allee effect in prey
Feng Rao
Nanjing Tech University, China
Keywords: Allee effect, diffusion, non-constant positive solution, pattern formation, Turing in-
stability
Abstract: This paper investigates complex dynamics of a predator-prey interaction model that
incorporates: (a) An Allee effect in prey; (b) the Michaelis-Menten type functional response between
prey and predator; and (c) Diffusion in both prey and predator. We provide rigorous mathematical
results of the proposed model including: 1) the stability of non-negative constant steady states; 2)
sufficient conditions that lead to Hopf/Turing bifurcations; 3) a prior estimates of positive steady
states; 4) the non-existence and existence of non-constant positive steady states when the model is
under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE
model to obtain a better understanding of the effects of diffusion on the stability. Our analytical
results show that the small values of the ratio of the prey’s diffusion rate to the predator’s diffusion
rate are more likely to destabilize the system, thus generate Hopf-bifurcation and turing instability
that can lead to different spatial patterns. Through numerical simulations, we observe that our
model, with or without Allee effect, can exhibit extremely rich pattern formations that include but
not limit to stripes, spotted patterns, symmetric patterns. In addition, the strength of Allee effects
also plays an important role in generating distinct spatial patterns.
References
[1] Akcakaya, H.R., Arditi, R., Ginzburg, L.R., Ratio-dependent predation: an abstraction that
works, Ecology 76 (1995): 995-1004.
[2] Kuang, Y., Beretta, E., Global qualitative analysis of a ratio-dependent predator-prey system, J.
Math. Biol. 36 (1998): 389-406.
[3] Hsu, S.B., Hwang, T.W., Kuang, Y., Global analysis of the Michaelis-Menten type ratio-
dependent predator-prey system, J. Math. Biol. 42 (2001): 489-506.
[4] Xu, R., Chaplain, M.A.J., Persistence and global stability in a delayed predator-prey system with
Michaelis-Menten type functional response, Appl. Math. Comput. 130 (2002): 441-455.
[5] Wang, W.M., Liu, Q.X., Jin, Z., Spatiotemporal complexity of a ratio-dependent predator-prey
system, Phys. Rev. E 75 (2007): 051913.
[5] Meng, X.Z., Li, Z.Q., Nieto, J.J., Dynamic analysis of Michaelis-Menten chemostat-type com-
petition models with time delay and pulse in a polluted environment, J. Math. Chem. 47 (2010):
123-144.
[6] Rao, F., Wang, W.M., Dynamics of a Michaelis-Menten-type predation model incorporating a
prey refuge with noise and external forces, J. Stat. Mech.: Theory Exp. 2012 (2012): P03014.
[7] Turing, A.M., The chemical basis of morphogenesis, Philos. Trans. R. Soc. Lond. Ser. B: Biol.
Sci. 237 (1952): 37-72.
[8] Kang, Y., Castillo-Chavez, C., Dynamics of SI models with both horizontal and vertical trans-
missions as well as Allee effects, Math. Biosci. 248 (2014): 97-116.
63
Modeling lentiviral infection and viral latency in the brainduring antiretroviral therapy
Weston Roda
Department of Mathematical and Statistical Sciences, University of Alberta
Keywords: mathematical model, viral dynamics, brain macrophage, HIV-1, SIV, combination
antiretroviral therapy (cART)
Abstract: HIV-1 replication and latency in different reservoirs is a continuing challenge in the
care of patients with HIV/AIDS. A mathematical model was developed to describe and predict the
viral dynamics of HIV-1 and SIV infection within the brain during effective combination antiretro-
viral therapy (cART). The mathematical model was based on the biology of lentiviral infection of
brain macrophages and used to describe the dynamics of transmission and progression of lentiviral
infection in brain. Previous reports quantifying total viral DNA and RNA levels in brain from
HIV-1 and SIV infections were used to calibrate the mathematical model predicting productively
and latently infected brain macrophages from primary infection.
References
[1] B. B. Gelman, J. G. Lisinicchia, S. Morgello, E. Masliah, D. Commins, C. L. Achim, et al Neu-
rovirological correlation with HIV-associated neurocognitive disorders and encephalitis in a HAART-
era cohort J. Acquir. Immune. Defic. Syndr. 62(5) (2013): 487-495
[2] H. GÃ3mez-Acevedo, M. Y. Li, S. JacobsonMultistability in a model for CTL response to HTLV-
I infection and its implications to HAM/TSP development and prevention Bull. Math. Biol. 72(3)
(2010): 681-696
[3] F. González-Scarano, J. Martin-Garcia The neuropathogenesis of AIDS Nat. Rev. Immunol.
5 (2005): 69-81
[4] M. A. Nowak, R. M. May Virus dynamics. Mathematical principles of immunology and virology
Oxford: Oxford University Press (2000)
[5] W. C. Roda, M. Y. Li, M. S. Akinwumi, E. L. Asahchop, B. B. Gelman, K. W. Witwer, et
al Modeling brain lentiviral infections during antiretroviral therapy in AIDS, J. Neurovirol. 23(4)
(2017): 577-586
[6] L. Rong, A. S. Perelson Modeling latently infected cell activation: viral and latent reservoir
persistence, and viral blips in HIV-infected patients on potent therapy PLoS Comput. Biol. 5(10)
(2009): e1000533
[7] P. Vivithanaporn, G. Heo, J. Gamble, H. B. Krentz, A. Hoke, M. J. Gill, et al Neurologic disease
burden in treated HIV/AIDS predicts survival Neurology 75 (2010): 1150-1158
[8] K. W. Witwer, L. Gama, M. Li, C. M. Bartizal, S. E. Queen, J. J. Varrone, et al Coordinated
regulation of SIV replication and immune responses in the CNS PLoS One 4(12) (2009): e8129
64
Population and vitellogenin dynamics of a honeybee colonyinfluencing division of labor
Marisabel Rodriguez*1, Yun Kang23, Robert E. Page4
School of Mathematical and Statistical Sciences2, Arizona State University, Tempe, AZ;
Simon A. Levin Mathematical Computational and Modeling Science Center3, Arizona State University,
Tempe, AZ;
Science and Mathematics Faculty, College of Integrative Sciences and Arts4, Arizona State University,
Mesa, AZ;
School of Life Sciences, Arizona State University, Tempe, AZ, USA
[email protected]; [email protected]; [email protected]
Keywords: Social insects, division of labor, honeybees, nutritional regulation, vitellogenin
Abstract: The complexity of honeybees has provided an ample study of different mechanism
affecting their population dynamics. Our goal is to provide further understanding of honeybees
and underlaying mechanisms of nutritional regulation influencing their age-based division of labor
and sudden or gradual changes in their populations within a colony. These mechanisms are affected
not only by intracolonial processes but also outside factors such as weather or change of season.
In this study, we presented a non-linear differential equation system that models the population
dynamics of population of brood, nurse bees, and foragers within a colony. The dynamics of these
populations are influenced by the available stored pollen in cells and the current levels of vitellogenin
(Vg) in the fat body of nurse bees. The size of the populations within the colony at a stable point
are directly dependent upon the increase of Vg levels per nurse bee. From our analytical analysis
and numerical simulations we obtained the following: (1) a honeybee colony can survive if the the
brood’s feeding rate is less than the efficiency of pollen collection rate by foragers for Vg production;
(2) decreasing the queen’s feeding rate decreases population size of brood, nurse bees, and foragers;
(3) Synthesis of Vg is necessary for colony survival (i.e. medium-high conversion rate of pollen to
vitellogenin); (4) Low mortality rate of nurse bees is critical to colony survival; (5) High transition
rate from nurse to forager is not sustainable for the colony in the long term.
65
Modeling the Importation and Local Transmission of Zika in Florida
Shigui Ruan
University of Miami
Keywords: Mosquito-borne disease, Zika virus, transmission dynamics
Abstract: Zika virus is transmitted by Aedes aegypti and Aedes albopictus mosquito species and
was imported to Florida and caused local outbreaks in 2016. We propose a deterministic model to
study its transmission dynamics as a mosquito-borne disease. The purpose is to model and mimic
the importation of Zika virus to Florida via travelers, local infections in domestic mosquitoes by
imported travelers, and finally non-travel related transmissions to local humans by infected local
mosquitoes. The model will be used to simulate the accumulative Zika cases in Florida. Since the
disease system is driven by a continuing input of infections from outside sources, orthodox analytic
methods based on the calculation of the basic reproduction number 0 are inadequate to describe
and predict their behavior. Via steady-state analysis and sensitivity analysis, effective control and
prevention measures for Zika as well as other mosquito-borne diseases are tested. (Based on a joint
paper with J. Chen, J. C. Beier, R. S. Cantrell, C. Cosner, D. O. Fuller, Y. Guan, and G. Zhang).
66
Competitive outcomes of a double-structured model of two invasive speciesof mollusks: zebra and quagga mussel
Paul L. Salceanu
University of Louisiana at Lafayette
Keywords: Invasive species, coexistence, competitive exclusion
Abstract: We develop and use a mathematical model to investigate interactions and competitive
outcomes between two invasive species of mollusks: zebra mussel (Dreissena polymorpha) and
quagga mussel (Dreissena rostriformis bugensis). The model has both spatial structure (patches)
and temporal structure (age: juvenile and adult individuals). We show that the asymptotic behavior
of the discrete time model is as follows. When migration among patches does not take place, in
each patch one species eliminates the other, and it settles at a constant population size. When
migration does take place, we provide migration thresholds above which the two species of mollusks
coexist in each patch. Moreover, we show that, at least for very little migration, the coexistence
takes the form of global convergence of solutions to an interior equilibrium. Further, we investigate
both numerically and analytically how larger variations in the migration coeffcients might affect
this outcome.
References
[1] Q. Huang, H. Wang, A. Ricciardi, and M. A. Lewis, Temperature and Turbidity-Dependent
Competitive Interactions Between Invasive Freshwater Mussels, Bulletin of Mathematical Biology,
78 (2016), 353—380.
[2] H.L. Smith, P. Waltman, Perturbation of a globally stable steady state, Proc. AMS 127(2)(1999),
447—453.
67
A mathematical model of interaction of pelagic algae, benthic algaeand nutrients in an oligotrophic shallow aquatic ecosystem
Junping Shi
Department of Mathematics, College of William and Mary,
Williamsburg, VA 23187-8795, USA
Keywords: Reaction-diffusion model, Pelagic algae, Benthic algae, Nutrients, Environmental pa-
rameters, Algal biomass density
Abstract: A coupled system of ordinary differential equations and partial differential equations
is proposed to describe the interaction of pelagic algae, benthic algae and one essential nutrient in
an oligotrophic shallow aquatic ecosystem with ample supply of light. The existence, uniqueness
and stability of non-negative steady states are shown, and these results characterize some threshold
conditions for the regime shift. The influence of environmental parameters on algal biomass density
is also considered, which is an important indicator of algal blooms. This is a joint work with
Jimin Zhang (Heilongjiang University) and Xiaoyuan Chang (Harbin University of Science and
Technology).
References
[1] Zhang, Jimin, Junping Shi, and Xiaoyuan Chang. A mathematical model of algae growth in
a pelagic benthic coupled shallow aquatic ecosystem. Journal of Mathematical Biology (2017), to
appear. (DOI: 10.1007/s00285-017-1168-8)
68
Existence and uniqueness of similarity solutions of a generalizedheat equation arising in a model of cell migration
Tracy L. Stepien & Hal L. Smith*
School of Mathematical and Statistical Sciences, Arizona State University
Abstract: A model of cell sheet migration in the context of wound healing leads to a nonlinear
generalization of the heat equation =
()for some integer , the cases = 1; 2; 3 being
most notable in applications. We examine similarity solutions of this equation which reduces the
pde to a nonlinear second order ode on the half line with Neumann boundary conditions at both
ends under suitable assumptions. The relevance of this infinite domain problem with cell migration
will be explained. We generalize the above-mentioned ode boundary value problem and show that
it has a unique solution using dynamical systems techniques including Wazewski’s principle.
69
Travelling waves in a model for the growth of Phytophthora
Eva Stadler
Department of Mathematics, Technical University of Munich
Co-authors: Hartmut Schwetlick, Johannes Müller
Keywords: nonlinear hyperbolic equation, travelling waves
Abstract: We consider a model for the growth of the fungus-like plant pathogen Phytophthora. It
has been observed experimentally that the density of Phytophthora varies behind the interface of
the front. From a correlated random walk for the tips of the fine filaments in which Phytophthora
grows, we derive a nonlinear hyperbolic equation with delay modeling the growth of Phytophthora
[1] and investigate running fronts. We find a crucial dependence on the parameters: if the splitting
rate of the tips is no larger than the rate at which the tips change their direction, the front satisfies
a monotone fixed point operator equation [3]. In this case, we use Weinberger’s approach [5] to
show existence of monotone travelling waves. If, however, the splitting rate of the tips is larger
than the rate at which the tips change their direction, the model exhibits a non-monotone nonlinear
operator. We show existence of travelling waves, adapting the methods of Thieme [4] and Li et al.
[2]. A striking result is the fact that the travelling wave is not necessarily monotone.
References
[1] A. Henkel, J. Müller, C. Pötzsche, Modeling the spread of Phytophthora, J. Math. Biol. 65
(2012): 1359-1385.
[2] B. Li, M.A. Lewis, and H.F. Weinberger, Existence of traveling waves for integral recursions
with nonmonotone growth functions, J. Math. Biol. 58 (2009): 323-338.
[3] H.R. Schwetlick, Travelling fronts for multidimensional nonlinear transport equations, Ann. Inst.
Henri Poincaré Analyse non linéaire 17 (2000): 523-550.
[4] H.R. Thieme, Density-dependent regulation of spatially distributed populations and their asymp-
totic speed of spread, J. Math. Biol. 8 (1979): 173-187.
[5] H.F. Weinberger, Long-time behaviour of a class of biological models, SIAM J. Math. Anal. 13
(1982): 353-396.
70
Modeling the Migration of Astrocytes During Retinal Development
Tracy Stepien
Department of Mathematics, University of Arizona, Tucson, AZ
Keywords: partial differential equations, embryonic development, retinal astrocytes, cell migra-
tion, population distribution
Abstract: Retinal vasculature is essential for adequate oxygen supply to the inner layers of the
retina, the light sensitive tissue in the eye. In embryonic development, formation of the retinal
vasculature via angiogenesis is critically dependent on prior establishment of a mesh of astrocytes,
which are a type of brain glial cell. Astrocytes emerge from the optic nerve head and then migrate
over the retinal surface as a proliferating cell population in a radially symmetric manner. Astrocytes
begin as stem cells, termed astrocyte precursor cells (APCs), then transition to immature perinatal
astrocytes (IPAs) which eventually transition to mature astrocytes. We develop a partial differential
equation model describing the migration of astrocytes where APCs and IPAs are represented as two
subpopulations. Numerical simulations are compared to experimental data to assist in elucidating
the mechanisms responsible for the distribution of astrocytes.
References
[1] T. Chan-Ling, Y. Chu, L. Baxter, M. Weible II, and S. Hughes In vivo characterization of astro-
cyte precursor cells (APCs) and astrocytes in developing rat retinae: Differentiation, proliferation,
and apoptosis, Glia 57 (2009): 39—53.
[2] M. Fruttiger, Development of the retinal vasculature, Angiogeneis 10 (2007): 77—88.
[3] C. Tao and X. Zhang, Development of astrocytes in the vertebrate eye, Dev. Dynam. 243 (2014):
1501—1510.
71
Extinctions in Large Populations under Periodic and ChaoticEnvironmental Forcing
Ivan Sudakov
Department of Physics, University of Dayton
Keywords: population, dynamical systems, mass extinction, Lotka-Volterra system, Lorenz system
Abstract: We develop a resource model for a large population of species which generalizes the well
known model [1] and takes into account species self-regulation, extinctions, and time dependence
of resources.
The model parameters depend on the state of its environment via time dependent coefficients.
If the resource turnover rate is large enough, the model reduces to a Lotka-Volterra system. If
we remove self-limitation effects for the Lotka-Volterra system, one finds that a single species
can survive only in a population for certain fixed environmental parameters. This model considers
environmental forcing through the average environmental temperature changes (a periodic function
of time). To simulate chaotic time forcing we assume that the environmental temperature can be
obtained by chaotic trajectories of the noisy Lorenz system, a rough model of atmospheric dynamics.
We found that when the population reaches the maximal biodiversity, the risk of mass ex-
tinctions, even under small environment changes, strongly increases. Random, chaotic or periodic
environment oscillations thus can dramatically affect biodiversity.
References
[1] J. Huisman and F.J. Weissing, Nature 402, 407 (1999).
72
Can infectious pathogens drive their host populations into extinction?
Horst R. Thieme
(joint work with Alex Farrell, Jim Collins, and Amy Greer)
Arizona State University
Keywords: incidence function, host decline, tiger salamanders, maximum likelihood fits
Abstract: Amphibian decline and disappearance have renewed interest in the part infectious
diseases (without Allee effects or reservoirs) have in the extinction of their host species. In simple
SI epidemic and endemic models, three classes of incidence functions are identified for their potential
to be associated with host extinction: Upper density-dependent incidences are never associated with
host extinction. Power incidences that depend on the numbers of infectives and susceptibles by
powers strictly between 0 and 1 are associated with initial-constellation-dependent host extinction
for all parameter values. Homogeneous incidences, of which frequency-dependent incidence is a
very particular case, and power incidences are associated with global host extinction for certain
parameter constellations and with host survival for others. This leaves the question undecided that
motivated this analysis, namely whether ranavirus epidemics can drive tiger salamander populations
into extinction. Laboratory infection experiments with salamander larvae are equally well fitted
by power incidences and certain upper density-dependent incidences such as the negative binomial
incidence and do not rule out homogeneous incidences such as an asymmetric frequency-dependent
incidence either.
73
Structural and Practical Identifiability Analysis of ZikaEpidemiological Models
Necibe Tuncer
Florida Atlantic University
Keywords: Zika virus, structural and practical identifiability analysis, parameter estimation, arbovirus-
diseases
Abstract: The Zika virus (ZIKV) epidemic has caused an ongoing threat to global health security
and spurred new investigations of the virus. Use of epidemiological models for arbovirus diseases
can be a powerful tool to assist in prevention and control of the emerging disease. In this article, we
introduce six models of ZIKV, beginning with a general vector-borne model and gradually including
different transmission routes of ZIKV. These epidemiological models use various combinations of
disease transmission (vector and direct) and infectious classes (asymptomatic and pregnant), with
addition to loss of immunity being included. The disease induced death rate is omitted from
the models. We test the structural and practical identifiability of the models to find whether
unknown model parameters can uniquely be determined. The models were fit to obtained time
series data of cumulative incidences and pregnant infections from the Florida Department of Health
Daily Zika Update Reports. The average relative estimation errors (ARE) were computed from
the Monte Carlo simulations to further analyze the identifiability of the models. We show that
direct transmission rates are not practically identifiable, however, fixed recovery rates improve
identifiability overall. We found ARE low for each model (only slightly higher for those that
account for a pregnant class), and help to confirm a reproduction number greater than one at the
start of the Florida epidemic. Elasticity of the reproduction numbers suggest that the mosquito
to human ratio, mosquito lifespan, and biting rate have the greatest potential for reducing the
reproduction number of Zika, and therefore corresponding control measures need to be focused on.
74
Understanding the Dynamics of Opinions in a Fully-Mixed Population
Rebecca C. Tyson
University of British Columbia Okanagan
Keywords: ordinary differential equations, opinion dynamics
Abstract: Opinions on a subject with just two sides can nonetheless be held with different degrees
of conviction, which leads to different patterns of influence when individuals interact. Individuals
with more strongly-held opinions can have greater influence than those with moderate opinions, or
less, if others are wary of extreme views. We use a differential equation model to understand how
the distribution of opinions evolves under various interaction and influence scenarios. In particular,
we explore the conditions that lead to polarisation (the division of a population into two camps
each holding only the corresponding extreme view) and centering (a population largely distributed
on more moderate opinions on both sides of an issue).
References
[1] B.O. Baumgaertner, R.C. Tyson, and S.M. Krone (2017) Spatial opinion dynamics and the
effects of two types of mixing arXiv: 1704.05012v1
75
Impact of Spatially Heterogeneous Temperature on Dengue Epidemics
Naveen K. Vaidya
Department of Mathematics and Statistics, San Diego State University
Keywords: Dengue epidemics, Diffusion model, Spatially heterogeneous temperature, Threshold
dynamics
Abstract: Growing spatial spread of dengue, a mosquito-borne disease, has been a major in-
ternational public health concern. In this talk, I will present a mathematical model to describe
the impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. To es-
tablish the global threshold dynamics of the model, we formulate the basic reproduction number
for homogenous temperature and the infection invasion threshold for heterogeneous temperature.
I will also present numerical simulation results to demonstrate how the spatially heterogeneous
temperature affects the disease dynamics.
76
Rich dynamics exhibited by predator-prey systems provided withadditional food supplements in the presence of inhibitory effect:
Applications to pest control
D. K. K. Vamsi
Department of Mathematics and Computer Science Sri Sathya Sai Institute of Higher Learning
Prasanthinilayam, A.P., India, 515134
Keywords: Supplement feeding, Diversionary feeding, Eco-friendly methods, Species conservation,
Pest eradication
Abstract: Ecological and biological conservation of living systems has been an active area of re-
search over the years by agriculturalists, biologists and mathematicians. One of the studies involves
additional food supplement feeding (also called as diversionary feeding) for the purpose of biological
(wildlife in some cases) conservation. The idea in this approach is to distract (thereby supplement)
the wildlife from predating upon the other species with the end goal of wildlife conservation. On
the other hand in agricultural entomology, insect control and optimization, additional food is sup-
plemented as a tool for effective pest control thereby achieving the biological control. The study
of these ecosystems is usually done using the predator-prey systems. In nature, we find situations
wherein the group defense (toxicity) of the prey reduces the predation rate. This type of behavior of
the prey is also known as inhibitory effect of the prey. Biological conservation of such predator-prey
systems in the presence of additional food supplements is quite challenging and interesting. In this
paper, we consider an additional food provided predator-prey system which is a variation of the
standard predator-prey model in the presence of the inhibitory effect of the prey. The predators
functional response is assumed to be of Holling type IV (considering the inhibitory effect). This
model is analyzed to understand the inherent dynamics of the system. The findings suggest that
the quality and quantity of additional food provided to the predators play a very significant role in
determining the eventual state of the ecosystem. The outcomes of the analysis suggest eco-friendly
strategies to eco-managers for biological conservation of living systems with specific applications to
pest control.
77
Model of Bovine Babesiosis in Cattle
P. van den Driessche
Department of Mathematics & Statistics, University of Victoria, Canada
Keywords: Bovine Babesiosis, Disease control strategy, Global stability, Target reproduction num-
ber
Abstract: Ticks are currently having longer seasonal activity and expanding geographic range
due to climate change, resulting in an increase in tick-borne diseases. Bovine Babesiosis (BB) in
cattle is caused by the transmission of protozoa of Babesia spp. by ticks as vectors. Juvenile cattle
(less than 9 months of age) have resistance to BB, rarely show symptoms, and acquire immunity
upon recovery. A model of the dynamics of BB transmitted by the cattle tick that includes juvenile
and adult cattle is formulated as a system of ordinary differential equations. Basic reproduction
numbers are calculated and it is proved that if these are below the threshold value of one, then
BB dies out. However, above the threshold value, the disease may approach an endemic state, and
control measures are suggested by determining target reproduction numbers using Columbia data
from the literature.
Joint work with C.M. Saad-Roy and Z. Shuai.
78
Examining the dynamic consequences of evolution in responseto a prolonged environmental disturbance
A. Veprauskas
University of Louisiana at Lafayette
Keywords: Darwinian dynamics, lethal effects, sublethal effects, surrogate species, predator-prey
system
Abstract: Prolonged exposure to a disturbance such as a toxicant has the potential to result
in rapid evolution of toxicant tolerance in many short-lived species. This evolution may allow
a population to persist at higher levels of the toxicant than is possible without evolution. Here
we apply evolutionary game theory to Leslie matrix models to obtain Darwinian equations that
couple population and evolutionary dynamics. We use these models to consider how the evolution
of tolerance to a disturbance may change the population dynamics of both the focal population
and interacting populations. We provide an application to Daphnia and determine the conditions
under which a Daphnia population can persist by evolving toxicant tolerance. We then extend this
idea to a predator-prey system in which the prey evolves in response to a toxicant but the predator
does not due to different time scales. We consider how evolution in the prey species impacts the
population dynamics of the predator species. This model is inspired by marine mammals which
have significantly longer lifespans relative to their food sources.
79
Modeling allele effects in a transgenic mosquito populationduring range expansion
Melody Walker
Virginia Tech
Keywords: Allee effect, Gene drive, mathematical model
Abstract: Mosquitoes are vectors for many diseases that cause significant mortality and morbidity
across the globe including malaria, dengue fever and Zika. As mosquito populations expand their
range into a new area, they may undergo mate-finding Allee effects such that their ability to
successfully find a mate becomes increasingly difficult at low population densities. With new
technology such as CRISPR-Cas9, creating target specific gene modification is much more reliable
and feasible than prior to its existence. We develop a mathematical model to investigate the
effects of releasing transgenic mosquitoes into newly established low-density mosquito populations
where infection is present as a means of disease control via vector elimination. Our model consists
of two life stages (aquatic and adults), which are further divided into three genetically distinct
groups: homogeneous wild type alleles, and both heterogeneous and homogeneous transgenic genes
that cause female infertility. We perform analytical and numerical analyses on the equilibria to
determine the level of saturation needed to eliminate mosquitoes in a given area. Additionally, we
identify critical population levels below which the spread of disease is ceased in these expanded
populations. This model demonstrates the potential for a gene drive system to reduce the spread
of vector-borne diseases by eliminating newly established mosquito populations.
80
Impact of bacterial hyperinfectivity on cholera epidemicsin spatially heterogeneous environments
Xueying Wang
Department of Mathematics, Washington State University
Keywords: Cholera models, hyperinfectivity, spatial heterogeneity
Abstract: In this work, we develop a new modeling framework to study the impact of bacterial
hyperinfectivity on cholera epidemics in spatially heterogeneous environment. Our model is built on
a reaction-advection-diffusion system to represent spatiotemporal dynamics of cholera transmission,
and incorporate bacterial hyperinfectivity and spatial heterogeneity. First, we define the basic
reproduction number R0 and establish the global threshold dynamics based on R0. Second, theglobal attractivity of the unique endemic equilibrium is discussed when the spatial environment is
homogeneous and waning cholera immunity, advection and intrinsic growth of bacteria are ignored.
Third, the dependence ofR0 on model parameters are analyzed by theoretical and numerical means.Our result highlights importance of hyperinfectivity and its interplay with spatial heterogeneity.
Particularly, our findings indicate ignoring hyperinfectivity may underestimate the risk of infection.
This is joint work with Feng-Bin Wang.
References
[1] X. Wang and F.-B. Wang„ Impact of bacterial hyperinfectivity on cholera epidemics in spatially
heterogeneous environments, submitted
81
Zika and dengue: the optimal vaccination ratewhen antibody enhancement considered
Jianhong Wu
Laboratory for Industrial and Applied Mathematics, York University, Canada
Keywords: Vector-borne disease co-circulation, antibody enhancement, vaccination
Abstract: Zika virus co-circulates with dengue in tropical and sub-tropical regions. Cases of
co-infection by dengue and Zika have been reported, the implication of this co-infection for an
integrated intervention program for controlling both dengue and Zika must be addressed urgently.
Here, we formulate a mathematical model to describe the transmission dynamics of co-infection
of dengue and Zika with particular focus on the effects of Zika outbreak by vaccination against
dengue among human hosts. Our analysis determines specific conditions under which vaccination
against dengue can significantly impact the Zika outbreak peak, and speed up the Zika outbreak
peak timing. Our results call for further study about the co-infection to direct an integrated control
to balance the benefits for dengue control and the damages of Zika outbreak.
References
[1] Tang, B. et al. Implication of vaccination against dengue for Zika outbreak. Sci. Rep. 6, 35623;
doi: 10.1038/srep35623 (2016).
82
Evolution of Social Cooperation of Microorganisms
Zhijun Wu
Department of Mathematics, Iowa State University
Keywords: evolution of cooperation, evolutionary game theory, evolutionary dynamics simulation,
spatial effects on cooperation
Abstract: Evolution of cooperation of biological species is an active research subject in evolution-
ary biology and ecology. Evolutionary game theory is a powerful modeling and simulation tool for
the study of ecology and evolution. Here, we use a lab-developed population of two yeast strains,
called the cooperator and cheater strains, to demonstrate the nature of the game that can be played
by the yeast strains and how cooperation can be maintained in such a population. We review the
lab experiments as well as previous computer simulations. We present our recent simulation results
on spatial effects on cooperation between the yeast strains when the interactions among the yeast
cells are restricted to their small neighborhood. Our results show that cooperation is increased
when the interactions are spatially restricted whether the game is of a prisoner’s dilemma, snow
drifting, or mutual benefit type. We also show when spatially restricted, groups of cooperators are
able to sustain and expand as group sizes become large, while groups of cheaters fail to expand and
tend to collapse.
References
[1] M. Nowak, Five rules for the evolution of cooperation, Science 314 (2006): 1560-1563
[2] J. Gore, H. Youk, A. van Oudenaarden, Snowdrift game dynamics and facultative cheating in
yeast, Nature 459 (2009): 253-256
[3] Y. Huang, Z. Wu, Game dynamic model for yeast development, Bull Math Biol 74 (2012):
1469-1484
[4] M. Wang, Y. Huang, Z. Wu, Simulation of yeast cooperation in 2D, Bull Math Biol 78 (2016):
531-555
83
Disease Extinction Versus Persistence in Discrete-time Epidemic Models
Abdul-Aziz Yakubu
Howard University, Washington, DC 20059, USA
Abstract: In this talk, we will focus on discrete-time infectious disease models in populations
that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations. When
R0 1 and the demographic population dynamics are asymptotically constant or under geometricgrowth (non-oscillatory), we prove global asymptotic stability (GAS) of the disease-free equilibrium
(DFE) of the disease models. When R0 1, we prove uniform persistence of the disease, and
the existence of a unique endemic equilibrium (EE). We apply our theoretical results to specific
discrete-time epidemic models that are formulated for SEIR infections, cholera in humans, and
anthrax in animals. Our simulations show that the EE of each of the three specific disease models
is asymptotically stable whenever R0 1.
84
Dynamical Analysis on an Autoimmune Disease Modelvia Model Reduction
Wenjing Zhang
Department of Mathematics and Statistics, Texas Tech Univeristy
Keywords: model order and parameter reduction, relapse-remission autoimmune disease, multiple
limit cycles.
Abstract: In this paper, we apply order reduction and parameter reduction on an autoimmune
disease model with relapse-remission behavior to show the advantage of these reductions. The
reduced models not only inherit the intrinsic relapse-remission pattern, but also allow sophisticated
mathematical analysis to reveal more complex dynamical behaviors such as bifurcation of multiple
limit cycles, which gives new insights in the autoimmune disease symptoms. Our analysis shows
that the quasi-steady-state assumption (QSSA) is an approximation of the slow invariant manifold
between the zero-order and the first-order asymptotic expansion based on geometric singular per-
turbation theory. The QSSA is able to keep the intrinsic dynamical behavior of the original system
and is much easier to use in practice than iterative methods for asymptotic expansion. However, it
may alter the determining parameter ranges, which is acceptable if the analysis is focused on the
qualitative behavior of the system. Moreover, the formulas for the parameter reductions can be
used to identify complex dynamics such as multiple limit cycles bifurcation in the original model.
85
Modelling the fear effect in predator-prey interactionswith adaptive avoidance of predators
Xingfu Zou
Department of Applied Mathematics, University of Western Ontario
London, ON, Canada
Keywords: Prey-predator interaction, fear effect, anti-predation response, maturation delay, equi-
librium, stability, bifurcation
Abstract: Recent field experiments on vertebrates showed that mere presence of a predator would
cause a dramatic change of prey demography. Fear of predators increases the survival probability
of prey but leads to a cost of prey reproduction. Based on the experimental findings, we propose
a predator-prey model with the cost of fear and adaptive avoidance of predators. Due to the
age structure, the model turns out to be a system of delay differential equations. By analyzing
the model, we gain some insights on how the anti-predation response of the prey will affect the
population dynamics of both prey and predators. This is a joint work with Dr. Xiaoying Wang.
86
Posters
A Mathematical Model to Study the Role of Osteocytesin the Bone Remodeling Process
Iris Alvarado
University of Texas at Arlington
Keywords: bone remodeling, osteocytes, WNT canonical pathway, sclerostin, spatio-temporal
model
Abstract: The skeleton is a very important organ that needs to be continuously remodeled due
to microdamage, changes in mechanical loading, or mineral homeostasis [1]. The bone remodeling
process maintains the structure and function of the skeletal system. Understanding how the process
works can give insight on why bone diseases exist, how they can be prevented, and what therapies
may help overcome such diseases. Evidence suggests osteocytes have the ability to sense and respond
to changes in external mechanical loading and as a result are able to initiate the bone remodeling
process. Furthermore, when microdamage is present in the bone structure, osteocyte apoptosis
plays an important role in the initiation of the bone remodeling process [2]. Osteocytes are known
to release scelorstion, an inhibitor of the WNT canonical pathway. This important pathway has
recently been discovered as a key signaling pathway for bone formation [3] and potential therapeutic
route for bone diseases such as osteoporosis [4]. The mathematical model results show that the
addition of WNT canonical pathway promotes the differentiation of the osteoblast precursor cells.
Additionally, the removal of the WNT pathway co-receptors, reduces the concentration of active
osteoblast, thus, the amount of bone formation and decreasing the production of sclerostin increases
bone formation. The results of the mathematical model are in agreement with in results found in
literature.
References
[1] Manolagas, S. C., 2000. Birth and death of bone cells: basic regulatory mechanisms and
implications for the pathogenesis and treatment of osteoporosis 1. Endocrine reviews 21 (2), 115-
137.
[2] Bellido, T., 2014. Osteocyte-driven bone remodeling. Calcified tissue international 94 (1), 25-34.
[3] Kramer, I., Halleux, C., Keller, H., Pegurri, M., Gooi, J. H., Weber, P. B., Feng, J. Q., Bonewald,
L. F., Kneissel, M., 2010. Osteocyte wnt/-catenin signaling is required for normal bone home-
ostasis. Molecular and cellular biology 30 (12), 3071-3085.
[4] Kim, J. H., Liu, X., Wang, J., Chen, X., Zhang, H., Kim, S. H., Cui, J., Li, R., Zhang, W.,
Kong, Y., et al., 2013. Wnt signaling in bone formation and its therapeutic potential for bone
diseases. Therapeutic advances in musculoskeletal disease 5 (1), 13-31.
[5] Buenzli, P. R., Pivonka, P., Smith, D. W., 2011. Spatio-temporal structure of cell distribution
in cortical bone multicellular units: a mathematical model. Bone 48 (4), 918-926.
88
A quantitative model for the impact of zooplankton diel vertical migrationon the vertical carbon flux of the biological pump
Kevin Archibald
Woods Hole Oceanographic Institution, Department of Biology
Keywords: marine biogeochemistry, biological pump, numerical models
Abstract: One pathway of the biological pump that remains largely unquantified in many models
of carbon export is the action of diel vertical migrations (DVM) of zooplankton, by which carbon
is actively transported from the euphotic zone to the mesopelagic. Zooplankton DVM contributes
to the vertical flux of carbon to below the euphotic zone when biomass that was grazed at the
surface is deposited at depth as either fecal pellets or metabolic dissolved inorganic carbon (DIC).
Here, we present a quantitative global model for the export of carbon out of the surface ocean,
both by passive sinking of biogenic particles and the active transport by zooplankton DVM, to
assess the effect of DVM on the biological pump. The DVM module is driven by a surface food web
model of production and export using diagnostic satellite measurements of NPP, algal biomass,
and size structure. The annual mean of the modeled export flux from the base of the euphotic
zone was 9.99 3.2 PgC/yr, which represents an 87% increase over the export flux that does not
include the contribution of zooplankton DVM. The model predicts a global annual mean export
ratio of 0.18 0.09. The effect of DVM activity is primarily a respiratory phenomenon, which
depends on metabolism at depth. The production of DIC by vertically migrating zooplankton
in the mesopelagic accounts for an average of 91% of the DVM-mediated export flux, while fecal
pellet production in the mesopelagic accounts for only 9%. The modeled DVM-mediated flux varied
greatly over the global domain and accounted for a greater fraction of the total export in areas
where NPP was lower. The results of this model indicate that zooplankton DVM is an important
pathway for the export of carbon out of the surface ocean as part of the biological pump. The
reported results are taken from a baseline model. Experiments on model sensitivity, as well as the
effects of temperature and oxygen concentration, are underway.
89
Sensitivity analysis on an updated model of Aedes aegypti abundance
Hannah Biegel
Department of Mathematics
University of Arizona
Keywords: mosquito control, Aedes aegypti, population dynamics, sensitivity analysis
Abstract: We perform sensitivity analysis on a recent model of Aedes aegypti mosquito abundance
[1], using meteorological data from two different locations, San Juan, Puerto Rico and Tucson,
Arizona. The model was shown to be in good agreement with surveillance trap data in Puerto Rico
when the following components were included: (i) previously laid eggs that have not desiccated are
likely to hatch and develop after rainfall [2,3], although too much rain can counteract this effect by
washing away eggs; (ii) adult survival is expected to depend on relative humidity (RH) [4,5].
The work presented here builds on previous sensitivity analysis, performed on a similar model
of Ae. aegypti abundance that used only temperature and precipitation [6]. We focus on the new
components listed above and identify parameters that significantly affect predicted adult abun-
dance. In particular, we observe that narrowing survival temperature thresholds for the egg stage
and narrowing the RH-dependent temperature survival thresholds for the adult stage significantly
decrease adult abundance, independently of one another. Additionally, we notice that when more
eggs are hatched after rain during a time when the weather does not support mosquito survival,
the onset of high abundance of the mosquito population is delayed. This analysis suggests that the
model could be improved with a more accurate understanding of the role of relative humidity on
the adult survival rate; future studies could investigate the role of removing dormant eggs when
climate conditions do not support mosquito development.
References
[1] Lega, J., H.E. Brown, and R. Barrera, Aedes aegypti (Diptera: Culicidae) Abundance Model
Improved with Relative Humidity and Precipitation-Driven Egg Hatching, Journal of Medical En-
tomology 54.5 (2017): 1375-1384.
[2] Barrera, R., M. Amador, V. Acevedo, B. Caban, G. Felix, and A.J. Mackay, Use of the CDC
Autocidal Gravid Ovitrap to Control and Prevent Outbreaks of Aedes aegypti (Diptera: Culicidae),
Journal of Medical Entomology, 51.1 (2014): 145-154.
[3] Barrera, R., M. Amador, V. Acevedo, R.R. Hemme, and G. Félix, Sustained, Area-Wide Control
of Aedes aegypti Using CDC Autocidal Gravid Ovitraps, American Journal of Tropical Medicine and
Hygiene, 91.6 (2014): 1269-1276.
[4] Canyon, D.V., J.L.K. Hii, and R. Müller, Adaptation of Aedes aegypti (Diptera: Culicidae)
oviposition behavior in response to humidity and diet, Journal of Insect Physiology, 45.10 (1999):
959-964.
[5] Fouque, F., R. Carinci, P. Gaborit, J. Issaly, D.J. Bicout, and P. Sabatier, Aedes aegypti survival
and dengue transmission patterns in French Guiana, Journal of Vector Ecology, 31.2 (2006) 390-399.
[6] Brown, H.E., R. Barrera, A.C. Comrie, and J. Lega, Effect of Temperature Thresholds on
Modeled Aedes aegypti (Diptera: Culicidae) Population Dynamics, Journal of Medical Entomology,
54.4 (2017): 869-877.
90
Modelling of cell-cell adhesions using a non-local integro-PDE model:Derivation and steady states
Andreas Buttenschön
University of Alberta
Keywords: integro-PDEs, cell-cell adhesion, space-jump process, steady-states
Abstract: Cellular adhesions are one of the fundamental biological interactions between cells
and their surroundings. However, the continuum modelling of cellular adhesions has remained
mathematically challenging. In 2006 Armstrong et. al. proposed a mathematical model in the form
of an integro-partial differential equation. This model was successful at replicating Steinberg’s cell
sorting experiments, and since has been used in models of cancer invasion and morphogenesis.
In this poster, I present a derivation of the non-local cell-cell adhesion model from an underlying
stochastic random walk. The key concept of this derivation is a cell’s polarization vector. Several
key micro biological properties are included in the polarization vector. I will show how the choice
of these properties yields the original cell-cell adhesion model as proposed by Armstrong et. al.
but also other novel non-local models.
I will conclude by discussing symmetric steady states of the non-local cell-cell adhesion model
that are created by pitchfork bifurcations along the trivial solution branch.
This is joint work with T. Hillen.
References
[1] A. Buttenschön, T. Hillen, A. Gerisch, K. Painter, A space-jump derivation for non-local models
of cell-cell adhesion and non-local chemotaxis, Journal of Mathematical Biology (2017): 1-28
[2] N. Armstrong, K. Painter, J. Sherratt, A continuum approach to modelling cell-cell adhesion,
Journal of Theoretical Biology (2006): 98-113
91
Social Network Models of Task Switching in Social Insect Colonies:Effects of Social Interactions and Spatial Heterogeneity
Jun Chen
Arizona State University
Keywords: Social insects, Task switching, Dynamic spatial fidelity, Social network, Agent based
model.
Abstract: In insects social network, it must consider the balance of many conditions at the same
time, like efficient information transfer, spatial movement in the colony during the nest defense,
disease spreading and inhibition. These behaviors are similar human network system, which also
has to meet lots of different constraints simultaneously. Therefore, social insects network models
could be the way to understand the established and changes of human network system. In ants
colonies, workers have different tasks, such as maintenance, forager and brood care. Each individual
obtains a single task on the one time, and individual switches its task by interaction, because the
rate of interaction will be affected by environment and group size, then the spatial distribution is
important factor in the task allocation [1]. Therefore, our goal is that how the dynamic spatial
fidelity affect the task switch? We used Agent-based model to simulate ants contact and task
switching in different initial spatial fidelity cases with or without negative feedback situation, which
means ants won’t like to move to a crowded place. From the simulation data, we found the dynamic
spatial fidelity and spatial heterogeneity degree will be stable, and contact rate has strong linear
correlation with task switching rate and spatial heterogeneity degree. Also within-group contact
rate is much higher than between-group rate. In the future, we try to establish stochastic model
to do more theoretical analysis.
References
[1] Stephen W Pacala, Deborah M Gordon, and HCJ Godfray. Effects of social group size on
information transfer and task allocation. Evolutionary Ecology, 10(2):127165, 1996.
92
Attenuant and Resonant Cycles of Several Periodic Population Modelswith Allee Effect and Overstocking
Marina Chugunova
Department of Mathematics and Statistics, University of Calgary, Alberta, Canada
Keywords: Difference equation, periodic population model, attenuant and resonant cycles, Allee
effect
Abstract: In the last 20 years, the intensive studies of the population models with periodic environ-
mental parameters brought the mathematical population modelling to a new level of undestanding
of biological mechanisms behind the development of ecological systems.
Existence of attenuant and resonant cycles of these models provides tools for possible regulation of
that development. Including in the model such properties of biological species and environment as
Allee effect and overstocking provided even more insight into the nature of population dynamics.
In this poster, several population models with periodic parameters are considered, including the
modified Beverton-Holt model with Allee effect. Under certain conditions on the set of parameters,
there are shown to exist both attenuant and resonant cycles.
References:
[1] J. Cushing, S. Henson, Global dynamics of some periodically forced, monotone difference equa-
tions, J. Difference Equations Appl. 7 (2001): 859-872
[2] J. Cushing, S. Henson, A periodically forced Beverton-Holt equation, J. Difference Equations
Appl. 8 (2012): 1119-1120
[3] S. Elaydi and R. Sacker, Global stability of periodic orbits of nonautonomous difference equations
and population biology, J. Differential Equations 208 (2005): 258-273
[4] S. Elaydi and R. Sacker, Nonautonomous Beverton-Holt equations and the Cushing-Henson con-
jectures, J. Difference Equations Appl. 11 (2005): 337-346
[5] R. Kon A note on attenuant cycles of population models with periodic carrying capacity, J. Dif-
ference Equations Appl.10(8) (2004): 791-793
[6] R. Kon, Attenuant cycles of population models with periodic carrying capacity, J. Difference
Equations Appl. 11 (2005): 423-430
[7] S. Elaydi and R.Sacker, Population models with Allee effect: a new model, J. Biological Dynam-
ics 4 (2010): 397-408
[8] R. Sacker, Semigroups of maps and periodic difference equations, J. Difference Equations Appl.
16 (2010): 1-13
[9] R. Luis, S. Elaydi, and H. Oliveira, Non-autonomous periodic systems with Allee effects, J. Dif-
ference Equations Appl. 16 (2010): 1179-1196
[10] G. Gaut, K. Goldring, F. Grogan, C. Haskell and R. Sacker, Difference equations with the Allee
effect and the periodic Sigmoid Beverton-Holt equation revisited, J. Biological Dynamics 6 (2012):
1019-1033
[11] L. Assas, B. Dennis, S. Elaydi, E. Kwessi and G. Livadiotis, Stochastic modified Beverton-Holt
model with Allee effect II: the Cushing-Henson conjecture, J. Difference Equations Appl. 22 (2016):
164-176
93
Using Satellite Imagery and Internet Datafor Dengue Surveillance in Brazil
Jessica Conrad*, Carrie Manore, Sara del Valle, Amanda Zeimann, Nidhi Parikh, Geoffrey
Fairchild, and Eric Generous
Los Alamos National Laboratory
Keywords: Dengue, stochastic model, distributed lags, remote sensing, forecasting
Abstract: Dengue fever cases have been increasing in Latin America in the last 15 years. Trans-
mission patterns for dengue fever are dominated by annual outbreaks and persistent co-circulation
of different serotypes. As there is no vaccine commercially available yet for dengue fever outside of
Mexico [1], prevention and control measures are the most important mitigation strategies. In our
research, we seek to use predictive risk analysis to forecast dengue dynamics in Brazil, and explore
whether remote sensing data can improve disease forecasting. As this is a mosquito-borne disease,
we explore predictive data streams such as previous cases, weather, precipitation, vegetation, land
use, and remote sensing data. We analyze the contribution of each data stream to the forecast using
a distributed lag model constructed with the dlnm and gam packages in R. Successful forecasting
of dengue fever in Brazil can lead to more successful preemptive vector control programs and thus
reduce dengue cases each year.
References
[1] “Questions and Answers on Dengue Vaccines." World Health Organization, World Health Or-
ganization, www.who.int/immunization/research/development/dengue_q_and_a/en/
94
Using mathematical modeling to understand mechanismsof behavior change in cohorts of problem drinkers
Rebecca Everett
Center for Research in Scientific Computation
North Carolina State University
Keywords: Mathematical psychology, mechanisms of behavior change, personalized medicine
Abstract: Psychologists are interested in developing new and accessible techniques to treat prob-
lem drinkers, individuals with mild to moderate severity of alcohol use disorder. Understanding
the mechanisms of behavior change for drinking reduction can help healthcare providers implement
more effective interventions. Thus it is important to understand the crucial factors that initiate
and maintain this change process. We use mathematical modeling and clinical data to identify
cohorts of patients with similar underlying mechanisms of behavior change as well as investigate
the important factors that can influence a patient’s success in reducing their alcohol consumption.
95
The Impact of Virus Mutation in Chikungunya Transmission:A Mathematical Modeling Analysis
Xiaomei Feng
Department of Mathematics and Statistics, Center of Disease Modelling,
York University, Canada
Department of Mathematics, Yuncheng University, People’s Republic of China
xiaomei−[email protected]
Keywords: Chikungunya; Mutation; Parameter estimation; Sensitive analysis
Abstract: Chikungunya is caused by the Chikungunya virus (CHIKV) and transmitted to hu-
mans by infected Aedes mosquitoes. Although mainly reported in Africa, Asia and the Indian
subcontinent before 2013, it is now becoming a global public problem. Particularly, it caused ma-
jor outbreaks in several countries of the Americas in 2015. Moreover, recent evidence indicates
that CHIKV has a new variant, which was found in La Réunion, Italy, China. The role of the new
variant on the spread and control of CHIKV infection is not clear. In this paper, we introduce
a mathematical model to investigate the impact of virus mutation on the spread and control of
CHIKV. Then we use the model to fit the CHIKV epidemic data from Italy in 2007, which indicates
that the outbreak of CHIKV in Italy might be caused by the mutant strain. By comparing with
a previous model without the mutation strain, it is founded that there is an underestimate of the
basic reproduction number if virus mutation is not considered. The basic reproduction number
is estimated to be R0 = 21[95%CI : 25129 − 26225] The sensitivity analysis indicates that R0is mostly sensitive to the biting rate and mortality rate of mosquitoes. Moreover, for the two
characteristics of the mutant strain, the shortened extrinsic incubation period has no significance
influence on R0, but the probability of transmission from mosquitoes with mutant strain to humansdoes. Combining with the mutation rate, it implies that mosquitoes with mutant strain have more
transmission ability which will increase the risk of infection and epidemic size.
96
Identification of Color Categories and their Evolution
Nicole A. Fider
Mathematics Department at University of California, Irvine
Keywords: human color categorization, World Color Survey (WCS), language dynamics
Abstract: In the fields of psychology and linguistics, it is understood that speakers from a common
linguistic background use basic color categories and corresponding basic color terms to divide
and describe the color space. These categories give members of the population the ability to
communicate color information with each other, despite the fact that categories are not consistently
defined across individuals. The categories used by a population can evolve over time, and in fact
categories are not consistently formed across cultures (for example, the number of basic color
categories in different languages varies between 2 and 12). We present a mathematical method of
identifying a language’s set of color categories based on color-naming data provided by the World
Color Survey Data Archives. We also discuss the possible dynamics of category evolution and how
it can be related to the numerical data.
References
[1] Nicole Fider, Louis Narens, Kimberly A. Jameson, and Natalia L. Komarova, “Quantitative
approach for defining basic color terms and color category best exemplars," J. Opt. Soc. Am. A34,
1285-1300 (2017)
97
A Household Model of Cockroach Infestation and Its Effectson Atopic Asthma Symptoms
Karen Funderburk
Arizona State University
Applied Mathematics for the Life and Social Sciences
Keywords: compartment model, asthma, German cockroach, cockroach allergens, backward bifur-
cation
Abstract: According to the Center for Disease Control and Prevention (CDC), asthma is a signif-
icant health concern, and cockroaches are among the most common indoor pests, with its allergen
being present in 63% of U.S. households. Improper extermination of cockroaches and the associated
allergens has been shown to increase the occurrence of atopic asthma, a type of asthma triggered by
the exposure to allergens. I discuss a household model that was developed to study the dynamics
of cockroach infestations in a neighborhood of houses with individuals sensitized to the cockroach
allergen. I also discuss the evaluation of the impact of extermination and removal of allergens
in a household with recurrent atopic asthma; as well as how numerical simulations on the model
and sensitivity analysis on the basic reproductive number were used to examine the impact of key
parameter values. Finally, I will discuss the numerical backward bifurcation that was obtained and
explain why the results showed that it is more effective to prevent infestation of cockroaches, rather
to attempt to remove cockroaches once they have infested a house.
98
Modeling How Selection in One Trait Interfereswith Adaptation in Another
Kevin Gomez
Applied Mathematics, University of Arizona
Keywords: Population Genetics, Adaptation, Fitness, Linkage Disequilibria
Abstract: When beneficial mutations appear rapidly, distinct beneficial mutations often com-
pete rather than combine, because they are linked to different genetic backgrounds. Without
recombination, only beneficial mutations occurring on the fittest (relatively low frequency) genetic
backgrounds contribute. Traveling waves have been used to quantify the resulting rate of adap-
tation under asexual reproduction [1], with all beneficial mutations interchangeable (evolution in
one trait dimension of “relative fitness"). We developed a two-dimensional traveling wave model,
and used it to quantify the negative genetic correlations arising between fitness-related traits as
a consequence of linkage disequilibria, determining the extent to which adaptation in one trait is
slowed by adaptation in the other. The genotype-fitness landscape not only affects the speed of
adaptive evolution directly through mutation rates and selection coefficients, but also indirectly by
shaping linkage disequilibria between loci encoding different adaptive traits. Simulations are used
to confirm our analytical results.
References
[1] Desai, M. M., & Fisher, D. S., Beneficial mutation-selection balance and the effect of linkage on
positive selection, Genetics 176 (2007): 1759-1798
99
Modeling Effect of Seasonality on Avian Influenza Dynamics
Queen Harris
School of Mathematical and Statistical Sciences, Arizona State University
Tempe, Arizona, USA
Keywords: Avian Influenza, Reproduction Number, Asymptotic stability
Abstract: Avian Influenza, a contagious disease of animals caused by influenza viruses of the family
Orthomyxoviridae, continues to inflect major burden to the poultry industry across the world (the
devastating 2014-2015 avian influenza outbreak in many parts of the United States being a recent
notable example [1]). In this poster, a model for the spread of the lowly- and highly-pathagenic
strains of avian inflenza in a country, which takes into account the seasonal migratory nature of the
birds population, will be presented. Results for the theoretical analysis and numerical simulations
will also be presented.
References
[1] United States Department of Agriculture. Final Report for the 2014-2015 Outbreak of Highly
Pathogenic Avian Influenza (HPAI) in the United States.
https://www.aphis.usda.gov/animalhealth/emergency/presentation/finalreport14-15shortppt.pdf
[2] T. Necibe, M. Martcheva, and M. Barfield, Modeling Seasonality in Avian Influenza H5N1. J.
Biol. Sys. 21: (2013) 1340004-1 - 1340004-30
100
An improved mathematical model for prostate cancerunder intermittent androgen suppression therapy
Changhan He
Arizona State University
Keywords: Prostate cancer, differential equations, three-population model
Abstract: A standard treatment for advanced prostate cancer is the Androgen Deprivation Ther-
apy (ADT). This accounts for the fact that tumor cells’ growth is androgen-dependent, but the
development of androgen-independent tumor cells usually takes place and renders the treatment
ineffective after several years. Due to the reduction in the male hormone during treatment, unde-
sirable effects cause loss in quality of life. Intermittent Androgen Suppression Therapy, the idea
of alternating between on and off treatment period in accordance to the prostate specific antigen
level, was introduced after Huggins’ and Hodes’ Nobel medicine discovery in 1983. This has been
shown to give patients better life quality. Numerous mathematical models have been developed to
model the progression of prostate cancer during different treatments. We review two major efforts
in the last decade and propose a combinative model that incorporates main ideas from these two
approaches. We show that the new model outperform the previous models in both fitting and
predicting power.
101
Vertical distributions of coral reef fish larvae influence dispersaland connectivity
Christina M. Hernandez
MIT/WHOI Joint Program in Oceanography, Woods Hole Oceanographic Institution
Keywords: dispersal, connectivity, metapopulation, trait-based, behavior, individual based model
Abstract: For coral reef fish, like many bottom-associated marine taxa, the larval phase repre-
sents the primary dispersal opportunity. However, this life phase is difficult to study because of the
high mortality rates, widespread distribution, and low abundances of larval fish in offshore regions.
Biophysical individual based models (IBMs), such as the Connectivity Modeling System (CMS),
are a vital tool for understanding the mechanisms driving observed patterns of dispersal and con-
nectivity. Four biological scenarios were simulated in CMS to investigate the influence of a range
of realistic depth behaviors on the dispersal and connectivity of reef fish in the Caribbean: (1) a
control scenario with no depth behavior, (2) surface-dwelling larvae, (3) larvae evenly distributed
in upper 100m, and (4) larvae exhibiting ontogenetic vertical migration (OVM). Using both global
and Gulf of Mexico HyCOM data from 2005-2008, nightly releases of 1000 larvae were simulated
from each of 60 sites in the wider Caribbean, and larvae were tracked for a maximum of 55 days.
Results indicate that the even distribution and OVM behaviors lead to higher retention of larvae
near release sites and a more closed pattern of connectivity than the control and surface-dwelling
scenarios. Even distribution and OVM larvae were also subject to less seasonal variability in dis-
persal distance than the control and surface-dwelling larvae. Examination of dispersal kernels by
release site indicates that local patterns of dispersal and connectivity are the result of interactions
between depth behaviors and local hydrography.
102
Evolution of Treatment Resistance in Advanced Prostate Cancer
Khoa Dang Ho*, William J. Baker, Jonathan Trautman and John D. Nagy
School of Life Sciences, Arizona State University
Keywords: Cancer modeling, Data fitting, Treatment resistance
Abstract: Recurrent and advanced prostate cancers are typically treated with total androgen
blockade. However, androgen deprivation almost inevitably leads to castration resistance. Molec-
ular mechanisms of castration resistance have been elucidated. The most common of these mech-
anisms is amplification of the androgen receptor (AR) gene. But the ultimate cause of resistance
remains unknown. Two hypotheses have been suggested: (i) resistance arises from cell plasticity;
and (ii) resistance is caused by natural selection acting on mutant clones within the tumor. Here we
show that evolution by natural selection is likely to be the ultimate cause of treatment resistance
in prostate cancer. We studied 55 patients treated with intermittent androgen deprivation ther-
apy. During on-treatment phases, tumor aggressiveness, as measured by prostate specific antigen
(PSA) velocity, increases over sequential cycles. In contrast, during off-treatment phases, tumor
aggressiveness did not appear to vary when fit with an exponential model. However, the best-fit
Gompertz model suggests that carrying capacity of PSA tends to increase, whereas intrinsic tumor
growth rate tends to decrease, over sequential off phases. These observations are consistent with
treatment generating directional selection for castration resistance. These results corroborate a
predictive mathematical model of natural selection for AR expression under androgen deprivation.
Such a model promises to be a key tool in managing castration protocols to mitigate the effects of
treatment resistance in prostate cancer.
103
Mathematical modeling of tumor-CD4+-cytokine-host cells interactionswith treatments
Xiaochuan Hu
Department of Mathematics and Statistics, Texas Tech University
Keywords: Tumor, immunotherapy, cytokine, ordinary differential equations, global stability,
bistability
Abstract: Mathematical models of interactions between tumor cells, CD4+ T cells, cytokines, and
host cells are proposed to investigate the role of CD4+ on tumor regression. Our results suggest
that host cells along with the mechanism of production of CD4+ T cells play important roles in
driving tumor dynamics. Cancer cells can be eradicated if the tumor has a small growth rate and
is also not competitive. Treatments by either CD4+, cytokines, or a combination of the two are
applied to study their effectiveness. It is concluded that doses of treatments along with the tumor
size are critical in determining the fate of the tumor. Tumor cells can be eliminated completely if
doses of treatments by cytokine are large. The treatments are in general more effective if the tumor
size is smaller. Bistability is observed in all of the models with or without the treatment strategies
indicating that there is a window of opportunity for clearing off the tumor cells.
References
[1] Allen L.J.S. 2006. An Introduction to Mathematical Biology, Prentice-Hall, New Jersey, 2006
[2] Anderson L., Jang S. R-J., Yu, J. 2015. Qualitative behavior of systems of tumor-4+-cytokine
interactions with treatments, Math. Meth. Appl. Sci., 38, 4330-4344
[3] de Pillis L. et al. 2005. A validated mathematical model of cell-mediated immune response to
tumor growth, Cancer Res., 65(17): 7950-7958
[4] Eftimie R. et al. 2010. Anti-tumour Th1 and Th2 immunity in the rejection of melanoma, J.
Theor. Biol., 265: 467-480
[5] Eftimie R. et al. 2011. Interaction between the immune system and cancer: a brief review of
non-spatial mathematical models. Bull. Math. Biol., 73: 2-32
[6] Dudley ME. et al. 2002. Cancer regression and autoimmunity in patients after clonal repopu-
lation with antitumor lymphocytes, Science, 298: 850-854
[7] Niu, L. Chen, J., He, L., Liao, M., Yuan, Y., Zeng, J., Zuo, J., Xu, K., 2013. Combination
treatment with comprehensive cryoablation and immunotherapy in metastatic pancreatic cancer.
Pancreas 42(7), 1143-1149
104
Modeling the Early Clinical Progression of HantavirusPulmonary Syndrome
Krystin E. S. Huff*, Edward J. Allen and Linda J.S. Allen
Texas Tech University
Keywords: sensitivity analysis, stochastic differential equations
Abstract: Hantavirus pulmonary syndrome (HPS) is a zoonotic infectious disease caused by infec-
tion of hantavirus, a virus transmitted by specific rodents. Infection with HPS has a mortality rate
as high as 40%. A target-cell limited model describes the dynamics at the cellular level during the
early stages of infection. This model is a system of ODEs with healthy cells, infected cells and free
virus. When characterizing the clinical stages of HPS, some simplifying assumptions are made in
the target-cell limited model.ï¿12In particular, to compare with clinical data, the free viral level is
assumed to be proportional to the number of infected cells. Calculations indicate that the progres-
sion of HPS using the simplified model is similar to the actual clinical progression. A sensitivity
analysis of the simplified model indicates that the maximum infection level is sensitive to changes in
initial infection, rate of infection, and time to immune response. A stochastic differential equation
model of clinical HPS, where the infection rate satisfies a mean-reverting process, provides a better
understanding of the clinical progression.
105
Modeling Effects of Temperature and Vaccineon Dengue Transmission Dynamics
Enahoro Iboi
School of Mathematical and Statistical Sciences, Arizona State University.
Keywords: Dengue serotypes, vaccine effects, temperature effects, stability
Abstract: A vaccine (Dengvaxia R°) against dengue fever has recently been released by SanofiPasteur Ltd. The vaccine, which targets all four dengue subtypes with varying efficacies, has been
approved in 11 countries (including Mexico). This talk focuses on the use of mathematical modeling
approaches to gain insight into the impact of the aformentioned vaccine and temperature variability
on the transmission dynamics of the four dengue subtypes in a community. Theoretical properties of
the new deterministic model developed for this setting will be discussed, in addition to presenting
some numerical simulation results for the disease dynamics in a community. It will be shown,
using data from Oaxaca Mexico, that dengue incidence increases with increasing mean monthly
temperature in the range [22 − 25] ◦C, and decreases thereafter. Furthermore, the minimum
vaccine coverage needed for the effective control of the disease depends on the valus of the mean
monthly temperature values. This is a joint work with A. Gumel (ASU).
References
[1] E.A. Iboi and A.B. Gumel. Mathematical assessment of the roles of temperature and Dengvaxia
vaccine on the transmission dynamics of dengue serotypes. Submitted.
[2] N.L. Gonzalez-Morales, M. Nunez-Lopez, J. Ramos-Castanedaeda and J. X. Velasco-Hernández
(2017). Transmission dynamics of two dengue strains with vaccination scenarios. Mathematical
Biosciences. 287: 54-71.
106
Modeling Voting Dynamics in a Two-Party System:Person-To-Person Interactions and Media Consumption
Caleb Ignace
Applied Mathematics for the Life and Social Sciences, Arizona State University
Keywords: modeling, voting, election, two-party, social interaction, media consumption, homoge-
neous, discrete-time, Markov chain, deterministic
Abstract: Two models are developed driven entirely by mass media consumption or social inter-
action among voters and non-voters of two parties. Taking inspiration from the epidemiological
concept of the spread of a disease, we model the spread of an idea, i.e., that one should vote for a
given candidate, with a deterministic discrete-time Markov chain: the time step is a week, the state
vector represents a voting population and an affiliated, non-voting population of each party, and
the transition matrix represents movement between the four compartments with dynamic terms
dependent on population sizes. We assume that media consumption and social interaction among
the population of the system are homogeneous. Both the media-driven model and the interaction-
driven model are fit to poll data from the 2012 and 2016 presidential elections. The comparison
across the two elections indicates that the influence of each state population changes from one
election to another, but the response to media is similar in both elections.
107
Two-species competition with two different typesof diffusion and harvesting
Ilia Ilmer
University of Calgary
Keywords: Reaction-diffusion system, Partial Differential Equations, Competition, Harvesting,
Population dynamics, Stability, Carrying capacity driven diffusion
Abstract: We investigate the effect of harvesting effort on the two-species competition model
where both species are subject to a logistic growth law. Two different diffusion strategies and
several values of harvesting are considered. Both species may have different intrinsic growth rates
and carrying capacities. It is known that if the two species choose to compete with different dispersal
strategies, everything else equal, the one with the carrying capacity driven diffusion brings the other
species to extinction as shown in [1]. Similar results have been proven for certain cases of different
carrying capacities in [2]. We show that for two different diffusion strategies harvesting can provide
coexistence and preclude competitive exclusion and extinction. In addition, we consider examples
of different intrinsic growth rates and provide analysis of the model’s outcomes in each case.
References
[1] L. Korobenko and E. Braverman, On evolutionary stability of carrying capacity driven dispersal
in competition with regularly diffusing populations, J. Math. Biol., vol. 69, no. 5, pp. 1181-1206,
2014.
[2] E. Braverman, M. Kamrujjaman, and L. Korobenko, Competitive spatially distributed population
dynamics models: Does diversity in diffusion strategies promote coexistence?, Math. Biosci., vol.
264, no. 1, pp. 63-73, 2015.
[3] R. S. Cantrell, C. Cosner, and Y. Lou, Advection-mediated coexistence of competing species,
Proc. Roy. Soc. Edinburgh Sect. A, vol. 137, no. 3, pp. 497-518, 2007.
108
Dynamics of the Emerging Fungal Pathogen Batrachochytriumsalamandrivorans on the Eastern Newt
Md Rafiul Islam*, Angela Peace**
Department of Mathematics and Statistics, Texas Tech University
*[email protected],**[email protected]
Keywords: amphibian declines, emerging disease, epidemiological model, wildlife pathogen.
Abstract: We developed and analyzed a stage-structured Susceptible-Infection (SI) type disease
models for emerging fungal pathogen Batrachochytrium salamandrivorans (Bsal). Our models
included two routes of pathogen transmission: direct transmission via contact between infected
and susceptible individuals and environmental transmission via shed zoospores in the water. Unlike
previous models, we categorized individuals into multiple stages of infection (susceptible, latency,
and infectious). We found the invasion probability for Bsal (i.e., the basic reproductive number,
R0) into a population of the Eastern Newt. We performed numerical simulations and parametersensitivity analysis using Latin hypercube sampling and partial rank coefficient correlation.
109
Population dynamics in a fragmented landscape with small patches:The Bodie pikas
Sabrina F. Jones*, Elinor Sauer and John D. Nagy
School of Life Sciences, Arizona State University
Keywords: Dynamical systems, Incidence Function Model, Island biogeography, Metapopulations
Abstract: A population of American pikas (Ochotona princeps) inhabiting an anthropogenic land-
scape in the ghost mining town of Bodie, CA has historically been interpreted as a true metapopu-
lation where dispersal among patches of habitat plays a definitive role in its population dynamics.
However, this assumption has never been explicitly demonstrated; in fact, it has been challenged by
two competing hypotheses. The first suggests that, rather than patches being roughly equal in size
and connectivity as in a metapopulation, large patches act as mainlands, making the landscape a
classical MacArthur-Wilson island-mainland system. The second hypothesis suggests that observed
occupancy patterns are a result of spatially correlated extinction events; in this hypothesis, dispersal
plays a negligible role. Here we show, using 20 years of empirical patch occupancy data, that dis-
persal must be a key driver of the population dynamics of the Bodie pikas. Furthermore, a Hanski
Incidence Function Model, which has become a standard modeling framework for metapopulations,
fits the data better than do models of the other two hypotheses. In addition, the metapopulation
concept has much more predictive and explanatory power. The Bodie pika population is well-suited
to provide insight into fragmented population dynamics because it is distributed over discrete habi-
tat patches, and we possess a series of high-quality censuses of the population from 1972 to 2010.
It has become a standard empirical model of the effects of habitat fragmentation; therefore, it is
critical that we have an accurate picture of the drivers of its population dynamics.
110
Evaluating the importance of body mass and habitat usein a trait-based model of foodweb dynamics
Amanda Laubmeier
North Carolina State University, Department of Mathematics
Keywords: parameter estimation, community ecology, modelling, allometry
Abstract: There is an immediate need for models which can predict the effect of changing ecological
communities, either due to species loss or migration, on trophic interactions. However, in order to
describe these diverse effects, we must develop generalizable models with foundations in key traits
that can be observed across study systems. We therefore consider the Allometric Trophic Network
(ATN) model, a Lotka-Volterra type model parameterized by body mass. We introduce a variation
on the ATN model which accounts for predator interference and habitat use. Using data from
greenhouse experiments, we estimate ATN model parameters. We are particularly interested in the
importance of spatial overlap in determining predators’ effects on one another and the implications
this might have in future model development.
This is a joint work with collaborators at the Swedish University of Agricultural Sciences in
Uppsala and California State University, Monterey Bay.
111
Coevolving cancer hallmarks: The angiogenic switch is modulated byclonal selection on proliferation
Aleesa Monaco*, Kalle Parvinen and John D. Nagy
School of Molecular Sciences, Arizona State University
Keywords: Adaptive dynamics, Cancer modeling, Evolution, Multiscale modeling
Abstract: Angiogenesis and dysregulated tissue homeostasis (proliferation) are canonical charac-
teristics of cancer. Both traits are thought to arise by clonal selection. However, natural selection’s
role in generating the angiogenic switch is not well understood. Here we show that the angiogenic
switch is likely to evolve by early positive selection on angiogenic ability which eventually becomes
reversed to negative selection in older tumors. Importantly, this reversal is itself driven by direc-
tional selection on proliferation ability. We study an established, general mathematical model of
tumor growth with angiogenesis. In the model, competing clones vary their ATP allocation to pro-
liferation, angiogenic signaling, and cell maintenance in a realistic way. Adaptive dynamics analysis
of this coevolutionary dynamic predicts that early tumors, in which proliferation rates have not yet
approached their evolutionary endpoint, experience positive selection for angiogenesis, conforming
to observations of the angiogenic switch in real tumors. However, as selection drives proliferation
towards its ESS, the once-favored angiogenic clones become susceptible to “free-rider" mutants,
which reallocate metabolic energy from angiogenesis production to proliferation. Selection on an-
giogenic ability therefore switches from positive to negative. The ultimate result would be necrosis
by vascular hypoplasia, a sort of “tumor-on-a-tumor" predicted in previous work. Simulations from
an analogous stochastic model, however, show that these deterministic endpoints are rarely real-
ized. Selection acts much more strongly on proliferation than on angiogenesis. As a result, tumors
often reach lethal size before negative selection on angiogenesis has much impact. Throughout its
clinical existence, a tumor’s angiogenic phenotype tends to ride along with a selective sweep acting
on proliferative ability. This model yields experimentally testable predictions and highlights the
importance of understanding coevolution of cancer hallmarks.
112
Co-infection Dynamics in a Novel Model of the HIV/Malaria Syndemic
Michele V. Moreno*, Clayton A. Grubb and John D. Nagy
Department of Life Sciences, Scottsdale Community College
Keywords: Discrete-time dynamical system, Epidemiology, Non-equilibrium model
Abstract: Together, HIV and malaria account for a substantial share of the effort and resources
devoted to global health improvement, particularly in sub-Saharan Africa. Despite great improve-
ments over the last 17 years, both diseases remain dominant public health threats. Further progress
requires an understanding of these diseases’ epidemic interactions, which are not fully characterized.
Therefore, we developed a novel semi-discrete-time model to investigate the interaction between
HIV and malaria in sub-Saharan Africa. Here we show that, in the absence of built-in physiological
interaction between the two diseases, a population-level syndemic effect exists in which the presence
of both diseases enhances their combined impact. Furthermore, HIV appears to be more responsive
to physiological perturbation due to the presence of malaria than malaria is to HIV. Our results
further the understanding of the co-infection dynamics of HIV and malaria and are pertinent to
the ongoing effort to combat both diseases.
113
Modeling of the tick population dynamics with the seasonaldevelopment process
Kyeongah Nah
Department of Mathematics and Statistics, York University, Canada
Keywords: Tick population, seasonal effects, periodic time delay, age-structure
Abstract: Seasonality influences development process of ticks in many ways: it affects the duration
of a life stages, host seeking behavior and hosts availability. Mathematical models have been
developed to formulate the stage-structured tick population growth incorporating the seasonal-
dependence. As an attempt to describe the mechanism of maturation in a realistic way, a recent
study [1] developed an age-structured model with time-dependent maturation delays.
In this study, we elaborate the age-structured model in [1] to incorporate time-dependent host
availability and feeding behavior. The age-structured model (partial differential equations) are then
reformulated into a DDE model (delay differential equations). By comparing numerical solutions
of the DDE model with its ODE analogy (ordinary differential equations), we observe that the
assumption on the mechanism of maturation lags affects the within-season dynamics, for example,
the peak time of the abundance of each life stage.
References
[1] X. Wu, F.M.G. Magpantay, J. Wu, and X. Zou, Stage-structured population systems with tem-
porally periodic delay, Mathematical Methods in the Applied Sciences 38 (2015): 3464-3481.
114
The Impact of Population Heterogeneity in Stochastic Models on theEmergence or Re-emergence of Infectious Diseases
Aadrita Nandi*, Dr J S Allen
Department of Mathematics and Statistics, Texas Tech University
Keywords: Emerging Disease, Epidemic model, Branching Process
Abstract: Recent outbreaks of emerging diseases such as SARS or MERS or of re-emerging dis-
eases such as measles or pertussis are often due to heterogeneity of the population in terms of
infectivity potential or susceptibility. In the case of SARS or MERS, superspreaders, highly infec-
tious individuals, were the major contributors to disease spread. However, in vaccine-preventable
diseases, such as measles or pertussis, recent outbreaks have occurred in populations with a large
proportion of susceptible individuals, where vaccine protection was low. Continuous-time Markov
chain epidemic models are formulated that account for these two different types of heterogeneity.
Theory from branching processes is used to approximate the probability of an outbreak when one
infectious individual from a population subgroup is introduced into the susceptible population.
Transmissibility and duration of infection as well as the amount of heterogeneity in the population
impact the probability of an outbreak. The models are applied to recent outbreaks of MERS and
measles.
References
[1] Allen L. J. S. A primer on stochastic epidemic models: formulation, numerical simulation, and
analysis. Infectious Disease Modeling, 206(1)
[2] De Serres Gaston et al. Higher risk of measles when the 1st dose of a 2-dose schedule of measles
vaccine is given at 12-14 months versus 15 months of age. Clinical Infectious Disease
115
Mathematical Analysis of Dengue-Chikungunya-Zika Transmission
Kamaldeen Okuneye
School of Mathematical and Statistical Sciences, Arizona State University (ASU)
Keywords: chikungunya, dengue, Zika virus, stability, Aedes aegypti, reproduction number, sen-
sitivity analysis, temperature, rainfall
Abstract: Aedes aegypti mosquito causes numerous diseases, including dengue fever (DENV),
chikungunya (CHIKV) and Zika virus (ZIKV), in humans and other (reservoir) hosts. The talk will
present a model for the transmission dynamics of the three diseases in a community. In addition to
testing three main hypotheses (namely, antibody-dependent enhancement, a DENV-CHIKV-ZIKV
competitive hierarchy and that the dengue vaccine could cross-react with ZIKV), the model will
be used to access the impact of temperature variability on the dynamics of the three diseases.
Relevant epidemiological and weather data from Mexico will be used in the illustrative numerical
simulations to be presented. This is a joint work with Professors A. B. Gumel (ASU) and J. X.
Velasco-Hernandez (UNAM, Mexico).
References
[1] Kamaldeen Okuneye, Jorge X. Velasco-Hernandez, Abba B. Gumel. The “unholy" Chikungunya-
Dengue-Zika Trinity: A Theoretical Analysis. Journal of Biological Sciences. (2017).
116
Sub-exponential growth for modeling plague:a case study of the 1904 Bombay plague
Tin Phan
Arizona State University
Keywords: mathematical modeling, plague dynamics, sub-exponential growth
Abstract: The 1904 bubonic plague in Bombay offers interesting contrasts to the Black Death,
especially in term of transmission. Previous studies use variations of the compartmental SIR
model to explain the transmission and dynamics of the Bombay plague. In this project, we use
a simple family of nested models based on logistic growth to fit the data. We further investigate
the possibility of sub-exponential growth at the district level with the additional usage of the
generalized growth model and the logistic patch model. Additionally, we apply the patch model to
study the effect of migration on the final epidemic size. Using statistical tests, our results support
the use of simpler logistic models for plague data fitting and suggest that, in general, the assumption
of exponential growth is sufficient, but sub-exponential growth should be considered in the case
of low-clustered population. However, when uncertainty in fitting is considered, sub-exponential
growth assumption is superior.
References
[1] William O Kermack and Anderson G McKendrick. A contribution to the mathematical the-
ory of epidemics. In Proceedings of the Royal Society of London A: mathematical, physical and
engineering sciences, volume 115, pages 700721. The Royal Society, 1927.
117
Two contrasting stage structured population modelsfor two pseudoscopion species from Argentina
Andrés O. Porta
Div. Aracanología. Museo Argentino de Ciencias Naturales
Keywords: Pseudoscorpions, Stage-Structured models
Abstract: Based on prospective data proceeding from two years sampling in two localities in Ar-
gentina, stage structured population models have been developed for two sympatric pseudoscorpion
species from Buenos Aires, Argentina: Dolichowithius (D.) argentinus Beier 1959 and Maxchernes
sp. While Maxchernes sp. exhibits a typical single reproductive cycle for year, D. (D.) argentinus
would be an r-strategist with two reproductive cycles in the favorable season. The resulting mod-
els constitute the first attempt to model pseudoscorpions population dynamics. This work shows
that arachnids from this order are well suitable as model organisms in the research of stage struc-
tured population models because of the easy sampling, accessible and well stablished taxonomy
and diversity of life stories.
118
Leaf-cutter ant nutritional effect on colony growth model:Protein-carbohydrate ratio intake and survival rate approach.
Angelica Marquez1, Marisabel Rodriguez*2, Komi Messan3, Yun Kang34
College of Engineering, University of Texas at El Paso1, El Paso, TX 79968;
School of Mathematical and Statistical Sciences2, Arizona State University, Tempe, AZ 85287;
Simon A. Levin Mathematical Computational and Modeling Science Center3, Arizona State University,
Tempe, AZ 85287;
Science and Mathematics Faculty, College of Integrative Sciences and Arts4, Arizona State University,
Mesa, AZ 85212
[email protected]; [email protected]; [email protected]; [email protected]
Keywords: Division of labor, complex adaptive behavior, leaf-cutter ants, nutritional regulation,
social insects.
Abstract: Social insects work together effectively for the survival of the colony by forming complex
adaptive behavioral connections between its members. Leaf-cutter foragers search leaves with varied
nutritional content (carbohydrate and protein) to feed the fungus which is then consumed by the
colony, based on the colony needs. Division of labor (DOL) in foraging efforts depends on colony
feedback and individual decisions. The objective of this study is to model the nutritional effects
in terms of protein to carbohydrate ratio on colony growth, therefore the effeteness on the DOL of
foraging efforts. To analyze the nutritional impact on colony growth and the related foraging DOL
we created a system of nonlinear adaptive ordinary differential equations. Division of labor can
generate up to two interior equilibria. Survival rate dependent on nutritional factors may generate
multiple interior equilibria between bistability dynamics and an interior saddle equilibrium. The
bistability dynamics may lead to low or relatively large biomass dependent on initial conditions.
High division of labor in conjunction with high death rate can drive the colony to collapse. The
nutrient collection directly affects the survival of the colony, where the colony can coexist in two
stable equilibria. Our results show the importance of the regulation of nutrient intake and division
of labor towards the success of the colony.
119
Influence of brood mortality on Honey Bee population dynamicsand the potential impact of insecticides
Armando Salinas
Arizona State University
[email protected] or [email protected]
Keywords: Honeybee, population dynamics, pesticides, brood mortality
Abstract: Vector-borne diseases account for approximately the 20% of all infectious diseases lead-
ing to the use of insecticides to control them. These chemical products not only affect mosquitoes
but other insects such as Honey bees, causing imbalances across most ecosystems around the world.
Honey bees (Apis mellifera) are responsible for pollinating nearly 80% of all food-producing plants,
therefore, the success or failure of a colony is vital to global food production. Previous mathematical
models ignored brood mortality and its influence on population dynamics. Our goal is to describe
the effect of insecticides on brood mortality and its possible effects over the entire population.
In order to do this, we constructed a compartmental model using non-linear ordinary differential
equations to describe brood birth, mortality, maturation and adult dynamics. We used data from
Harrison (1975-76) in order to see how well our model fits the data and estimate the parameters.
We found equilibria (and their conditions of existence and stability), and performed sensitivity
analysis on the equilibria. We also found the basic reproductive number R, where R 1 could
lead to proliferation, while R 1 could lead to colony collapse. Our results showed that in order
for the population to become extinct, a single brood, on average, live for half of a day, which is
unrealistic. Furthermore, sensitivity analysis showed that death of the adults has more influence
on extinction compared to the death of brood. This reaffirms other literatures’ findings that brood
mortality is not influential over a single season.
120
Mathematical Assessment of the Role of Vertical Transmissionand Temperature Variability on Dengue Transmission Dynamics
Rahim Taghikhani
School of Mathematical and Statistical Sciences, Arizona State University
Tempe, Arizona, USA
Keywords: Dengue, Vertical transmitted, Temperature, Stability, Reproduction Number, Bifurca-
tion
Abstract: Dengue, a viral disease transmitted to humans by adult female Aedes mosquitoes, affects
millions of people across the tropical and subtropical regions of the world. Data has shown that
dengue virus has been vertically (transovarially) transmitted from various species of adult Aedes
mosquitoes (including Aedes aegypti and Aedes albopictus, the main transmitters of dengue disease
in humans). This presentation is based on the design and use of a model for dengue transmission
dynamics that enables the assessment of the population-level impact of vertical transmission (in
both the vector and host population), as well as the effect of variability in local temperature on
the dynamics of dengue in a community. Theoretical and numerical simulation results will be
presented. In particular, it will be shown that vertical transmission has very marginal impact on
the disease dynamics. Furthermore, it will be shown that the effect of vertical transmission is
temperature-dependence. This is a joint work with Abba Gumel (ASU).
References
[1] M. Diallo, J. Thonnon, and D. Fontenille, Vertical transmission of the yellow fever virus by aedes
aegypti (diptera, culicidae): dynamics of infection in f-1 adult progeny of orally infected females,
Am. J. Trop. Med. Hyg, 62 (2000), pp. 251-156.
[2] M. Grunnill and M. Boots, How important is vertical transmission of dengue viruses by mos-
quitoes (diptera: Culicidae)?, J Med Entomol., 53 (2016), pp. 1-19.
[3] D. Shroyer, Vertical maintenance of dengue-1 virus in sequential generations of aedes albopictus,
J. Am. Mosq. Control Assoc, 6 (1990), pp. 312-314.
[4] R. Taghikhani and A. Gumel, Mathematical assessment of the role of vertical transmission and
temperature variability on dengue transmission dynamics.
121
Vector Transmission Model for Visceral Leishmaniasis
Mugdha Thakur
Simon A. Levin Mathematical, Computational and Modeling Sciences Center
Arizona State University, Tempe
Keywords: Visceral Leishmaniasis, PKDL, Persistence, Behavioral Resistance, Health Seeking
Behavior, Nonadherence
Abstract: In the developing countries of Eurasia, South and Central America, Visceral Leishmani-
asis (VL) is a neglected disease causing the deaths of millions of people. It is difficult to effectively
control this disease, since infection remains asymptomatic for most of the time after being exposed
to the parasite and since effectiveness of interventions is limited because of constrained resources.
In this study, we develop and analyze a novel mathematical model to effectively capture the trans-
mission dynamics of VL in India and thereby deduce an effective solution to optimal distribution of
resources to reach elimination targets set by WHO. The proposed model explicitly incorporate five
major mechanisms that characterize local transmission cycle in Indian state of Bihar. These mech-
anisms are (i) distinguishing individuals in early and late stages of infection (to effectively capture
difference between active and passive detection of cases), (ii) irregular treatment adherence levels
among the patients (to estimate the degree of incomplete treatment and impact of social cultural
issues), (iii) health seeking behavior of symptomatic individuals (to study role of socio-economic
factors), (iv) the impact of integrated vector control programs (such as bed-nets, indoor residual
spraying, and environmental management) and (v) behavioral resistance in sandflies (because of
insecticide dependent vector control measures). Furthermore, we study the impact of different
causes of nonadherence to treatment and found that unaccounted cases to nonadherence have sig-
nificant negative impact on the efficacy of the current integrated intervention measures for disease
elimination.
122
A new gravity model for spatial interaction: An applicationto highway flow estimation in the western United States
Craig Thompson
University of Arizona
Keywords: gravity model, spatial interaction, flow estimation, road travel
Abstract: Gravity models have been widely used to study spatial interactions between population
centers. The classical gravity model assumes the knowledge of origin-destination (OD) flows for
parameter calibration/inference. While this may be reasonable for some applications such as air
travel, it presents challenges for many other applications such as road traffic, where the observed
flow on road segments may involve traffic for multiple OD pairs. This paper proposes a novel
extension of the classical unconstrained gravity model, which improves its efficacy in predicting
spatial interactions when the observed flow between an OD pair involves interaction among multiple
OD pairs in a system. The modified gravity model, called the cumulative gravity model, was
calibrated along with the classic gravity model in a study of highway traffic in three different regions
of the western United States: Arizona only, 10 western US states, and 16 western US states. Both
models used a power decay function of distance and calibrated parameter values will be presented
and discussed. The cumulative gravity model performed better than the classic model, but the
improvement was only significant in the Arizona and 10 western US states networks. Removal of
commercial traffic from the data further improved the model’s performance. We will discuss these
modifications, as well as an application of the new gravity model to examine the impact of varying
travel distances on road travel and potential future research directions.
123
Modeling the Effects of Inflammation in Bone Fracture Healing
Imelda Trejo
Department of Mathematics, University of Texas at Arlington
Keywords: Homeostasis, fracture healing, molecular signaling, inflammation, macrophages, mes-
enchymal stem cells
Abstract: A new mathematical model is presented to study the early inflammatory effects in
bone healing. It consists of a system of nonlinear ordinary differential equations that represents the
interactions among macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis
of the model is performed to determine the equilibria and their corresponding stability properties.
There are three equilibria which represent the successful healing, nonunion, and dead tissue. A set
of numerical simulations is presented to support the theoretical results. The model is also used to
numerically monitor the evolution of a broken bone for different types of fractures and to explore
possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.
References
[1] Bailon-Plaza A and Van Der Meulen MC, A mathematical framework to study the effects of
growth factor influences on fracture healing, Journal of Theoretical Biology 212(2001): 191-209
[2] Kojouharov HV, Trejo I, and Chen-Charpentier B, Modeling the effects of inflammation in bone
fracture healing, AIP Conference Proceedings (forthcoming 2017)
[3] Schmidt-Bleek K, Kwee BJ, Mooney DJ, and Duda GN, Boon and bane of inflammation in bone
tissue regeneration and its link with angiogenesis, Tissue Engineering Part B: Reviews 21(2015):
354-364
124
Artificial Selection for Dispersal in Experimental Metapopulationsof Confused Flour Beetles (Tribolium confusum)
Sarah Ung*, Adam T. Hrabovsky, Michele V. Moreno, Kerry Calhoun, Sean Hamilton
and John D. Nagy
Department of Life Sciences, Scottsdale Community College
Keywords: Artificial evolution, Discrete-time dynamical system, Dispersal, Metapopulation dy-
namics
Abstract: In metapopulations, dispersal connects subpopulations residing in discrete patches of
habitat surrounded by uninhabitable matrix. In the 1970s Levins showed that metapopulation
persistence requires that colonization rates equal extinction rates, which in turn requires adequate
dispersal. Dispersal rate, on the other hand, is determined by evolutionary forces acting on individ-
ual fitness, not population persistence. The dynamics of this interplay are not entirely understood.
Here we investigate the precise nature of dispersal behavior in artificial metapopulations of con-
fused flour beetles (Tribolium confusum). We show that dispersal in T. confusum is highly plastic,
depending on environmental conditions. The key environmental determinant appears to be humid-
ity. During periods of high humidity, T. confusum disperse innately. That is, the probability that
an individual beetle disperses is not related to the number of dispersal avenues, but rather some
fixed behavioral tendency. In contrast, during periods of low humidity, dispersal is opportunistic:
beetles disperse at a rate that depends on availability of dispersal corridors. We also corroborate
the results of Ogden and others who suggest that dispersal can be artificially selected in this species,
which supports the conclusion of high heritability of dispersal behavior.
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Evaluating strategies for reversing CRISPR-Cas9 gene drives
Michael R. Vella
North Carolina State University
Keywords: evolution, population genetics, equilibria, stability
Abstract: A gene drive biases inheritance of a gene so that it increases in frequency within
a population even when the gene confers no fitness benefit. There has been renewed interest
in environmental releases of engineered gene drives due to recent proof of principle experiments
with the CRISPR-Cas9 system as a drive mechanism. Release of modified organisms, however,
is controversial, especially when the drive mechanism could theoretically alter all individuals of a
species. Thus, it is desirable to have countermeasures to reverse a drive if a problem arises. Several
genetic mechanisms for limiting or eliminating gene drives have been proposed and/or developed,
including synthetic resistance, reversal drives, and immunizing reversal drives. While predictions
about efficacy of these mechanisms have been optimistic, we lack detailed analyses of their expected
dynamics. We develop a discrete time model for population genetics of a drive and proposed genetic
countermeasures. Efficacy of drive reversal varies between countermeasures. For some parameter
values, the model predicts unexpected behavior including polymorphic equilibria and oscillatory
dynamics. The timing and number of released individuals containing a genetic countermeasure can
substantially impact outcomes. The choice among countermeasures by researchers and regulators
will depend on specific goals and population parameters of target populations.
References
[1] M.R. Vella, C.E. Gunning, A.L. Lloyd, & F. Gould. “Evaluating strategies for reversing
CRISPR-Cas9 gene drives." Scientific Reports (2017), in press.
126
Critical contact rate for vector-host-pathogen oscillation involvingco-feeding and diapause
Xue Zhang
Department of Mathematics & Statistics, York University
Toronto, Ontario, Canada, M3J 1P3
Department of Mathematics, Northeastern University
Shenyang, Liaoning, China, 110819
Keywords: Diapause, tick population dynamics, tick-borne disease, oscillation
Abstract: We consider a vector-host-pathogen interaction model for tick-borne infections such as
tick-borne encephalitis and Lyme disease. Since diapause always occurs after ticks are exposed to
a changed climatic condition including photoperiod and temperature, we introduce two time lags
during the process of development for ticks. We also consider co-feeding infection which takes place
horizontally between co-feeding ticks. We derive threshold conditions for disease persistence and
for the nonlinear oscillations in the tick population and in the diseased vector and host populations.
Our objective here is to use a simple mechanistic dynamic model to show diapause and co-feeding
infection may generate periodic and irregular oscillations even when seasonal variations of the
environmental conditions are ignored. These oscillations are not necessarily in synchrony with
the seasonality of vector development, and hence complicated oscillatory patterns of vector-borne
disease dynamics in the field and surveillance observations should be expected.
References
[1] A. Rizzoli, H. Hauffe, V. Tagliapietra, M. Neterler, Roberto R, Forest structure and roe deer
abundance predict tickborne encephalitis risk in Italy, PLoS One 4 (2009) e4336.
[2] C. Kiffner, W. Zucchini, P. Schomaker, T. Vor, P. Hagedorn, M. Niedrig, F. Rhe, Determinants
of tick-borne encephalitis in counties of southern Germany, Int J Health Geogr 9 (2010) 2001-2008.
[3] N. Bacaër, S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality: the
case of cutaneous leishmaniasis in Chichaoua, Morocco, J Math Biol 53 (2006) 421-436.
[4] P. Foley, J. Foley, Modeling susceptible infective recovered dynamics and plague persistence in
California rodent-flea communities, Vector Borne Zoonotic Dis 10 (2010) 59-67.
[5] WC Marquardt, Biology of disease vectors, 2nd Edition, Elservier Academic Press, USA, 2005.
[6] R. Rosà, A. Pugliese, Effects of tick population dynamics and host densities on the persistence
of tick-borne infections, Math Biosci 208 (2007) 216-240.
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