Mathematical models for plant disease epidemics
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Transcript of Mathematical models for plant disease epidemics
EPIDEMOLOGY AND DISEASE FORECASTING
MATHEMATICAL MODELS FOR FORECASTING PLANT DISEASE
EPIDEMICS
Speaker - Ashajyothi.M
EPIDEMIC
"Change in disease intensity in a host population over time and space.“
Interactions of the these 5 components play a key role.
.
Classification of epidemics
Type of reproduction of the pathogen Monocyclic Polycyclic Polyetic
POLYCYCLIC
MONOCYCLIC
Gymnosporangium juniperi virginianaelifecycle
DUTCH ELM DISEASEPOLYETIC EPIDEMICDUTCH ELM DISEASE POLYETIC EPIDEMIC
What will happen if an epidemic occurs?
What can we do about that?
Diseases - Major threats for crops around the world.
BENGAL FAMINE
IRISH FAMINE
Carry economical, environmental and social problems.
we study disease dynamics.....
Studying disease progress over time, where time (t) is modeled as a continuous variable rather than as a discrete variable.........
Make a simple yet realistic model .(Biology) We can solve it.(Math) We see what happens when we change parameters. To find a sustainable strategies to prevent the impact of the
diseases in crops.(Field application)
Mathematical tools used for modeling plant disease epidemics
The problem nature and epidemiologist specific questions determine the mathematical tool to be used (Kranz and Royle, 1978).
The commonly used mathematical tools are: Disease progress curves Linked Differential Equation (LDE) Area Under disease Progress Curve (AUDPC) computer simulation statistical tools, visual evaluations and pictorial assessment.
SIGMOID CURVE
BIMODAL CURVE
SATURATION CURVE
Growth models provide a range of curves that are often similar to disease progress curves.
(Van Maanen and Xu, 2003)
The growth models commonly used for temporal disease epidemics (Xu, 2006) are:
Monomolecular Exponential Logistic Gompertz
Monomolecular model
Given by Mitscherlich in 1909. Appropriate for modeling monocyclic epidemics (Forrest, 2007).
“Absolute change in rate of diesase is not proportional to the ‘y’ (disease intensity) but it is proportional to the ‘1-y’ (disease free intensity)”.
dy/dt = rM (1-y) dy / dt = absolute change in disease rM = rate parameter
(amount of initial inoculum * infection rate of unit inoculum) (1-y) = proportion of healthy tissue
MONOMOLECULAR DISEASE PROGRESS
Exponential model
This model is also known as the logarithmic or Malthusian model. Applied to describe the very early stages of most polycyclic epidemics (Forrest, 2007).
“ The absolute change in rate of disease is directly proportional to the disease intensity.”
dy/dt = rE y dy / dt = absolute change in disease
rE = rate parameter (infectiousness of diseased individuals, factors affecting disease) y = disease intensity
EXPONENTIAL DISEASE PROGRESS
Logistic model
Proposed firstly by Verhulst in 1838 to represent human population growth.
More appropriate for most polycyclic diseases.
“Absolute of rate in the change of disease is proportinal to the both disease intensity and disease free intensity”.
dy/dt = rLy(1-y) dy / dt = absolute change in disease
rL = rate parameter(infectious ness of diseased individuals ,factors affecting
disease) y = disease intensity
(1-y) = proportion of healthy tissue
LOGISTIC DISEASE PROGRESS
Gompertz model Given by B.Gompertz as an alternative to the logistic model. Appropriate for polycyclic diseases.
Gompertz model has an absolute rate curve that reaches a maximum more quickly and declines more gradually than the logistic models (Forrest, 2007).
dy/dt = ry ln(1/y) dy / dt = absolute change in disease rY = rate parameter (infetion rate) y = disease intensity
Examples of disease progress curves represented by monomolecular, exponential, logistic and Gompertz models.
Conclusion
Study ‘what if’ scenarios and provide decision-makers with a prior knowledge of consequence of disease incursions and impact of control strategies.
Frequently ignore relevant variables that affect the epidemic development (Xu, 2006),
e. g. Host growth, fluctuating environmental condition, length of latent and infectious period, etc. To be useful, models need to be fit for purpose and appropriately
verified and validated.
References:
1. Mathematical modeling tendencies in plant pathology, L. M. Contreras-Medina, Torres-Pacheco, R. G. Guevara-González, R. J. Romero- Troncoso, R. Terol-Villalobos and R. A. Osornio-Rios
2. Modelling plant disease epidemics, A. van Maanen and X.-M. Xu.
3. Plant pathology , 5th edition: Agrios,
4. Growth models for plant disease progress, http://www.aps.org.net
5. Class notes
6. www.google.com // images ( epidemiology, famines)
Thank you