SIR epidemic model with varrying total population size

We study the SIR epidemic model with varying total population size and constant immigration rate. We derive the sufficient conditions on parameters of the system to guarantee that the equilibrium points of the system are locally asymptotically stable or globally asymptotically stable. If the disease-free equilibrium point is stable, then the disease will not affect the population in the system. On the contrary, if the endemic equilibrium point is stable, the number of infectives will not change which means the infected rate equals to the recovery rate. Consequently, we can predict the disease’s behavior and the prevention program can be efficiently instituted.