Global analysis of a model of differential susceptibility induced by genetics

This paper is concerned with global analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals. We prove that this system has no periodic solutions and use the Poincaré index theorem to determine the number of rest points and their stability properties. It has been shown that multiple equilibria (bistability) occurs for suitable values of parameters. We also give some numerical examples of all possible bifurcations of this system.