GLOBAL STABILITY OF AN SEIS EPIDEMIC MODEL WITH BEDDINGTON-DEANGELIS INFECTION RATE

In this paper, the global dynamic behaviors of an SEIS epidemic model with Beddington-DeAngelis infection rate are investigated. This model takes into account constant recruitment, death from the disease, and the phenomenon of latency. Under some hypotheses, it is shown that the global dynamics is determined by the basic reproduction number $R_0$. If $R_0$ is less than unity, the disease-free equilibrium is both locally and globally stable and the disease dies out. If $R_0$ is greater than unity, sufficient conditions for the global stability of the endemic equilibrium are obtained by the geometric approach of Li and Muldowney. Some numerical simulations are also presented to confirm the analytical results.