Global stability of a generalized epidemic model

The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable — the global result has not been established previously.