An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate

作者：Wang, Xinli^*

来源：Discrete Dynamics in Nature and Society, 2015, 2015: 720682.

DOI：10.1155/2015/720682

• NONLINEAR INCIDENCE RATES
• BEHAVIOR

This paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemic equilibrium are first studied. Under the assumption of nonexistence of periodic solution, the global dynamics of the model is established: either the number of infective individuals tends to zero as time evolves or it produces bistability in which there is a region such that the disease will persist if the initial position lies in the region and disappears if the initial position lies outside this region. Computer simulation shows such results.

• 出版日期2015
• 单位上海理工大学