July  2007, 8(1): 161-173. doi: 10.3934/dcdsb.2007.8.161

Complex dynamics of a simple epidemic model with a nonlinear incidence

1. 

Science College, Air Force Engineering University, Xi'an 710051, China

2. 

Department of Mathematics, Xi'an Jiaotong University, Xi'an, 710049

3. 

Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3

4. 

Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

Received  December 2005 Revised  February 2006 Published  April 2007

A simple epidemic model with a nonlinear incidence rate and two compartments is studied. The backward bifurcation is described and the corresponding threshold is calculated. The Hopf bifurcation and Bogdanov-Takens bifurcation are analyzed and numerical evidences for the stable or unstable limit cycle are provided.
Citation: Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma. Complex dynamics of a simple epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 161-173. doi: 10.3934/dcdsb.2007.8.161
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