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.
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|
|Related URLs: |
|Depositing user: ||Pure Administrator|
|Date Deposited: ||11 Aug 2011 14:57|
|Last modified: ||04 Apr 2014 14:26|
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