Stability analysis of epidemic model with varrying total population size and constant immigration rate

Abstract

In this paper we study an SIR epidemic model with varying total population size and constant immigration rate. We investigate stability properties of the equilibrium points of this model and provide sufficient conditions under which the equilibrium points are locally stable or globally stable. If the disease-free equilibrium point is stable, then the population survives. On the other hand, if the endemic equilibrium point is stable, the number of infective will not change which means the infected rate equals the recovery rate. Thus, we may predict the disease's dynamic behavior and the prevention program can be efficiently instituted.