Complex dynamics of a simple epidemic model   with a nonlinear incidence

Jianquan Li; Yicang Zhou; Jianhong Wu; Zhien Ma

doi:10.3934/dcdsb.2007.8.161

Article Contents

2007, Volume 8, Issue 1: 161-173. Doi: 10.3934/dcdsb.2007.8.161

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Complex dynamics of a simple epidemic model with a nonlinear incidence

1.
Science College, Air Force Engineering University, Xi'an 710051
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

Received: November 30, 2005

Revised: January 31, 2006

Published: December 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 92D30, 34K20; Secondary: 34K25.

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