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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 154725, 14 pages
http://dx.doi.org/10.1155/2014/154725
Research Article

Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

School of Mathematical Sciences, Harbin Normal University, Harbin 150500, China

Received 8 October 2013; Accepted 17 December 2013; Published 20 January 2014

Academic Editor: Francisco Solís Lozano

Copyright © 2014 Xiaoming Fan. 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 discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number , we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.