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

Abstract EN

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.