Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 490437, 18 pages
doi:10.1155/2009/490437
The dynamics of the pulse birth in an SIR epidemic model with standard incidence
Juping Zhang
, Zhen Jin
, Yakui Xue
and Youwen Li
Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, China
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.