Stability of disease free sets in epidemic models

In this paper the attractivity properties of disease free subsets are considered in the context of disease transmission models. Sufficient conditions are derived for the existence of stable disease free subsets in a general compartmental disease transmission model. The conditions are stated in terms of the system linearized along the trajectories limited to a subset of disease free states. The proof is in the framework of the classical direct method of Lyapunov. As illustrations of the result a multigroup SIRS vaccination model and a Lotka–Volterra system with prey epidemic interaction are presented.