Global stability for a class of discrete SIR epidemic models

  • 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

    Related Papers:

  • 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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