Global analysis of an epidemic model with a constant removal rate

In this paper we consider an epidemic model, which is a reduced SIRS model with a constant removal rate of the infective individuals, for its qualitative properties which were not revealed in [W. Wang, S. Ruan, Bifurcations in an epidemic model with constant removal rate of the refectives, J. Math. Anal. Appl. 291 (2004) 775–793]. We first prove the uniqueness of closed orbits if they exist for this epidemic model. Then we discuss the qualitative properties of equilibria at infinity for global tendencies. Therefore, global dynamical behaviors of this system are obtained in the end.