Competitive exclusion and coexistence of multiple strains in an SIS STD model

In this paper we give a rather complete analysis for a two-sex, susceptible-infective-susceptible (SIS) sexually transmitted disease (STD) model with two competing strains, where the females are divided into two different groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterize the competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability of these equilibria. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium - that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability. This coexistence is globally stable or unstable if and only if the two boundary equilibria are both unstable both stable.