Global stability of a SIR epidemic model with nonlinear incidence rate and time delay

作者：Xu Rui^*; Ma Zhien

来源：Nonlinear Analysis: Real World Applications , 2009, 10(5): 3175-3189.

DOI：10.1016/j.nonrwa.2008.10.013

• SIR epidemic model
• Nonlinear incidence
• Time delay
• Stability

In this paper, a SIR epidemic model with nonlinear incidence rate and time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease free equilibrium is discussed. It is proved that if the basic reproductive number R(0) > 1, the system is permanent. By comparison arguments, it is shown that if R(0) < 1, the disease free equilibrium is globally asymptotically stable. If R(0) > 1, by means of an iteration technique and Lyapunov functional technique, respectively, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium.

• 出版日期2009-10
• 单位西安交通大学