Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population

In this paper, we propose a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population, which is derived from the continuous case by using the well-known backward Euler method and by applying a Lyapunov function technique, which is a discrete version of that in the paper by Prüss et al. [J. Prüss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B 6 (2006) 225–235]. It is shown that the global dynamics of this discrete epidemic model with latency are fully determined by a single threshold parameter.