Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 490437, 18 pages
doi:10.1155/2009/490437
Research Article

The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence

Juping Zhang,1,2 Zhen Jin,1 Yakui Xue,1 and Youwen Li1

1Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China
2School of Mechatronic Engineering, North University of China, Taiyuan, Shanxi 030051, China

Received 21 October 2008; Revised 6 February 2009; Accepted 29 April 2009

Academic Editor: Antonia Vecchio

Copyright © 2009 Juping Zhang 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

An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗<1. The infection-free periodic solution is unstable and the disease is uniform persistent if R∗>1. Our theoretical results are confirmed by numerical simulations.