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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 295060, 12 pages
http://dx.doi.org/10.1155/2012/295060
Research Article

The Global Behavior of a Periodic Epidemic Model with Travel between Patches

1School of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
2Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, Chongqing 400044, China

Received 3 March 2012; Accepted 14 May 2012

Academic Editor: Wing-Sum Cheung

Copyright © 2012 Luosheng Wen 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 establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio and two theorems on the global behavior: if < 1 the disease-free periodic solution is globally asymptotically stable and if > 1, then it is unstable; if > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.