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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 592821, 12 pages
http://dx.doi.org/10.1155/2013/592821
Research Article

Survival and Stationary Distribution in a Stochastic SIS Model

1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2Shanghai Medical Instrumentation College, Shanghai 200093, China

Received 10 October 2013; Accepted 12 November 2013

Academic Editor: Zhen Jin

Copyright © 2013 Yanli Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamics of a stochastic SIS epidemic model is investigated. First, we show that the system admits a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: when , we show how the solution spirals around the disease-free equilibrium of deterministic system under some conditions; when , we show that the stochastic model has a stationary distribution under certain parametric restrictions. In particular, we show that random effects may lead the disease to extinction in scenarios where the deterministic model predicts persistence. Finally, numerical simulations are carried out to illustrate the theoretical results.