Global stability for a class of discrete SIR epidemic models.

Math Biosci Eng

Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan.

Published: April 2010

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.

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Source
http://dx.doi.org/10.3934/mbe.2010.7.347DOI Listing

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