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The Scientific World Journal
Volume 2013, Article ID 871393, 5 pages
http://dx.doi.org/10.1155/2013/871393
Research Article

Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives

Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, Hebei 075000, China

Received 17 April 2013; Accepted 9 May 2013

Academic Editors: J. Banaś and M. M. Cavalcanti

Copyright © 2013 Junhong Li and Ning Cui. 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

An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compound matrix theory. Furthermore, the method of direct numerical simulation of the system shows that there is a periodic solution, when the system has three equilibrium points.