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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 172631, 11 pages
http://dx.doi.org/10.1155/2013/172631
Research Article

Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate

1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
2School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China
3College of Life and Environmental Science, Wenzhou University, Wenzhou 325035, China

Received 21 April 2013; Revised 23 May 2013; Accepted 23 May 2013

Academic Editor: Mark A. McKibben

Copyright © 2013 Yongli Cai 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

We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.