Abstract and Applied Analysis
Volume 2012 (2012), Article ID 132095, 12 pages
http://dx.doi.org/10.1155/2012/132095
Research Article

Global Stability of Two-Group Epidemic Models with Distributed Delays and Random Perturbation

Xiaoming Fan, Zhigang Wang, and Xuelian Xu

School of Mathematics Science, Harbin Normal University, Harbin 150025, China

Received 1 November 2011; Accepted 31 December 2011

Academic Editor: Norimichi Hirano

Copyright © 2012 Xiaoming Fan 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 discuss a two-group SEIR epidemic model with distributed delays, incorporating random fluctuation around the endemic equilibrium. Our research shows that the endemic equilibrium of the model with distributed delays and random perturbation is stochastically asymptotically stable in the large. In addition, a sufficient stability condition is obtained by constructing suitable Lyapunov function.