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A stochastic differential equation SIS epidemic model

Gray, Alison and Greenhalgh, David and Hu, L. and Mao, Xuerong and Pan, Jiafeng (2011) A stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics, 71 (3). pp. 876-902.

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Abstract

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.

Item type: Article
ID code: 29592
Notes: Changed last author
Keywords: susceptible-infected-susceptible model, pneumococcus , gonorrhea, stationary distribution, basic reproduction number, persistence, extinction, stochastic differential equations, Brownian motion, Probabilities. Mathematical statistics, Applied Mathematics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date deposited: 11 Aug 2011 13:57
Last modified: 26 Sep 2017 01:51
URI: https://strathprints.strath.ac.uk/id/eprint/29592
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