Global stability for a class of discrete SIR epidemic models - Yoichi Enatsu; Yukihiko Nakata; Yoshiaki Muroya (Mathematical Biosciences and Engineering)
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.