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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 2: 347-361. doi: 10.3934/mbe.2010.7.347
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Global stability for a class of discrete SIR epidemic models

  • 1.
    Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555
  • 2.
    Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555
  • Received: 01 July 2009 Accepted: 29 June 2018 Published: 01 April 2010

  • MSC : Primary: 34K20, 34K25; Secondary: 92D30.

  • 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.

    Citation: Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability for a class of discrete SIR epidemic models[J]. Mathematical Biosciences and Engineering, 2010, 7(2): 347-361. doi: 10.3934/mbe.2010.7.347

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