Global stability for a class of discrete SIR epidemic models
Yoichi Enatsu - Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan (email)
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.
Keywords: Backward Euler method, discrete SIR epidemic model, distributed delays,
globally asymptotic stability, Lyapunov functional.
Received: July 2009; Accepted: February 2010; Published: April 2010.
2013 5-year IF1.232