An SIRS Epidemic Model Incorporating Media Coverage with Time Delay

作者：Zhao, Huitao; Lin, Yiping^*; Dai, Yunxian

来源：Computational and Mathematical Methods in Medicine, 2014, 2014: 680743.

DOI：10.1155/2014/680743

• NONLINEAR INCIDENCE
• GLOBAL STABILITY
• DIFFERENTIAL EQUATIONS
• DYNAMICS
• TRANSMISSION
• BIFURCATION

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number R-0 < 1. However, when R-0 > 1, the stability of the endemic equilibrium will be affected by the time delay; there will be a family of periodic orbits bifurcating from the endemic equilibrium when the time delay increases through a critical value. Finally, some examples for numerical simulations are also included.

• 出版日期2014
• 单位周口师范学院; 昆明理工大学