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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.

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