An SIRS epidemic model of two competitive species

An autonomous SIRS epidemic model of two competitive species with interinfection of disease is formulated and analyzed. Some thresholds are identified and global asymptotic stability results of the bounded equilibria are proved. To the interior equilibrium, its local asymptotic stability is obtained. And under suitable conditions, it is proved that the model is uniformly persistent. Moreover, it is discovered that the interfinfection of disease is crucial to the dynamical behavior of the system, namely, when the two species coexist and the disease persists in both of them, and if the interinfection is removed, then three different cases may occur. 1.(1) The disease still persists in both species. 2.(2) The disease persists in one species, but dies out in the other species. 3.(3) The disease dies out in both species.