title: Global stability for a class of discrete SIR epidemic models.
abstract: In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model.
authors.affiliation: Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan. yo1.gc-rw.docomo@akane.waseda.jp
authors.forename: Yoichi
authors.initials: Y
authors.lastname: Enatsu
authors.forename: Yukihiko
authors.initials: Y
authors.lastname: Nakata
authors.forename: Yoshiaki
authors.initials: Y
authors.lastname: Muroya
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks; D006801:Humans; D008954:Models, Biological