Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 727168, 7 pages
doi:10.1155/2010/727168
Research Article

Persistence of an SEIR Model with Immigration Dependent on the Prevalence of Infection

Wenjuan Wang, Jingqi Xin, and Fengqin Zhang

Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China

Received 31 May 2010; Accepted 7 October 2010

Academic Editor: Guang Zhang

Copyright © 2010 Wenjuan Wang 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 incorporate the immigration of susceptible individuals into an SEIR epidemic model, assuming that the immigration rate decreases as the spread of infection increases. For this model, the basic reproduction number, R0, is found, which determines that the disease is either extinct or persistent ultimately. The obtained results show that the disease becomes extinct as R0<1 and persists in the population as R0>1.