Modeling for Science and Public Health, Part 2 NAGMS Council January 25, 2013 Stephen Eubank...
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Transcript of Modeling for Science and Public Health, Part 2 NAGMS Council January 25, 2013 Stephen Eubank...
Modeling for Science andPublic Health, Part 2
NAGMS CouncilJanuary 25, 2013
Stephen EubankVirginia Bioinformatics Institute
Virginia Tech
Infectious disease modeling has changed Then: coupled rate equations (SEIR)
– Ross, MacDonald, Kermack, McKendrick, Reed, Frost– nonlinear response, herd immunity & R0
– results like this:
Infectious disease modeling has changed Now: systems science perspective
– simulations with diverse, interacting parts– society, behavior, environment, demographics– results like this:
Networks represent systems of interacting entities
Vertices -> entitiesEdges -> interactions
Interactions change entities’ internal states and network structure changes, producing system-level dynamics.
Networks represent infectious disease epidemiology
Vertices -> peopleEdges -> proximity
Interactions change peoples’ health/beliefs/behavior and contacts change, producing epidemic dynamics.
Targeted interventions can berepresented as network changes
Vaccination
Messaging
Sequestration
Isolation
Vertex / edge choices represent many systems
0-5 year olds
school-age
adults
co-location
Vertex / edge choices represent many systems
vectors
livestock
humans
biting behavior
Vertex / edge choices lead to many* systems
female heterosexualnon injecting drug user
male bisexual injecting drug user
…
needle sharing,unprotected sex
* cf Hethcote, “A thousand and one epidemic models”, Frontiers in Math. Bio. (1994)
A complete solution is impossible
It would require 1.5 PB for 32 people with states (S,I,R)
(kN possibilities): the network correlates entities’ states.
Alice Bob Carol David Ellen probability of this configurationof states (today)
S S S R S 0.002
I S R R S 0.013
I I S S S 0.004
S I R S R 0.108
I I I R S 0.006
S R I S R 0.030
I S R R S 0.001
R R I S S 0.092
R I R I S 0.006
Agent-basedmodels
Compartmental models
Reaction-diffusion models
Compartmental models• emphasize aggregate, population outcomes• assume entities are indistinguishable &
averages are representative• produce equations of state
Reaction-diffusion models
• emphasize network structure• assume fixed detailed network• are “equation-free”
subgraph selection transmission tree reconstruction
Agent-based models•emphasize behavior•assume details are known•simulate a few instances
work workshoplunchcarpool
daycare
home home
bus school
car
Different models are appropriate for different questions
It’s better to have an approximate answer to the right question than an exact answer to the wrong question.
- John Tukey
Leveraging transdisciplinary insights
• Physics:– How do transition properties depend on network topology?– Scale-free networks only have an epidemic phase
• Chemistry:– How do aggregate properties of well-mixed systems
emerge?– coupled rate equations (structured compartmental model)
• Discrete math, combinatorics, computer science:– How can I approximate solutions efficiently?– feasibility of solving/approximating classes of problems
Regional variations matter …
… and depend on aggregate demographics
% attack rate
School contact networks matter …
H. Xia, J. Chen, M. Marathe, H. Mortveit (2011) Synthesis and refinement of detailed subnetworks in a social contact network for epidemic simulations. Proc. Int’l Conf. on Social Computing, Behavioral modeling and Prediction, College Park, Maryland.
… even though they affect only details
DegreeShortest Paths
Clustering
Household caregiving behavior matters…
A Marathe, B Lewis, J Chen, S Eubank Sensitivity of Household Transmission to Household Contact Structure and Size. PLOS One, 6(8): e22461
… but is hard to observe
Not “assume a spherical cow …”
What to expect from the new infectious disease models
Expect simplificationsthat reflect Public Health understanding, not mathematical / computational convenience
MODEL
Not “turn to page 79 of your textbooks …”
Scientific modeling is an art and a research program. Expect creativity,not pat solutions.
What to expect from the new infectious disease models