An SIRS model with a nonlinear incidence rate

作者：Jin, Yu; Wang, Wendi^*; Xiao, Shiwu

来源：Chaos Solitons & Fractals, 2007, 34(5): 1482-1497.

DOI：10.1016/j.chaos.2006.04.022

The global dynamics of an SIRS model with a nonlinear incidence rate is investigated. We establish a threshold for a disease to be extinct or endemic, analyze the existence and asymptotic stability of equilibria, and verify the existence of bistable states, i.e., a stable disease free equilibrium and a stable endemic equilibrium or a stable limit cycle. In particular, we find that the model admits stability switches as a parameter changes. We also investigate the backward bifurcation, the Hopf bifurcation and Bogdanov-Takens bifurcation and obtain the Hopf bifurcation criteria and Bogdanov-Takens bifurcation curves, which are important for making strategies for controlling a disease.

• 出版日期2007-12
• 单位湖北文理学院