A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positiv...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2011-01, Vol.71 (3), p.876-902
Main Authors: GRAY, A., GREENHALGH, D., HU, L., MAO, X., PAN, J.
Format: Article
Language:English
Subjects:
Computer simulation
Determinism
Differential equations
Disease models
Disease transmission
Epidemics
Epidemiology
Mathematical models
Modeling
Parametric models
Stochastic models
Studies
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Summary:In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positive solution I(t) and establish conditions for extinction and persistence of I(t). We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
ISSN:0036-1399
1095-712X
DOI:10.1137/10081856X