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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 262535, 9 pages
http://dx.doi.org/10.1155/2014/262535
Research Article

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

1Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Enshi, Hubei 445000, China
2Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei 445000, China

Received 20 April 2013; Revised 27 December 2013; Accepted 30 December 2013; Published 23 February 2014

Academic Editor: Aura Reggiani

Copyright © 2014 Mei Yan and Zhongyi Xiang. 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 consider a nonautonomous SEIR endemic model with saturation incidence concerning pulse vaccination. By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. Finally, numerical simulations are given to illustrate the main theoretical results and it shows that pulse vaccination plays a key role in the disease control.