2007•Discrete and Continuous Dynamical Systems - BRequires access

Complex dynamics of a simple epidemic model with a nonlinear incidence

Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma

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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Key concepts: Hopf bifurcation, Bogdanov–Takens bifurcation, Limit cycle, Bifurcation, Biological applications of bifurcation theory, Saddle-node bifurcation, Mathematics, Epidemic model