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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
    Related URLs:
      Depositing user: Pure Administrator
      Date Deposited: 11 Aug 2011 14:57
      Last modified: 04 Apr 2014 14:26
      URI: http://strathprints.strath.ac.uk/id/eprint/29592

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