# American Institute of Mathematical Sciences

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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