Dynamics of an ultra-discrete SIR epidemic model with time delay

  • Received: 12 March 2017 Published: 01 June 2018
  • MSC : Primary: 37N25; Secondary: 39B82

  • We propose an ultra-discretization for an SIR epidemic model with time delay. It is proven that the ultra-discrete model has a threshold property concerning global attractivity of equilibria as shown in differential and difference equation models. We also study an interesting convergence pattern of the solution, which is illustrated in a two-dimensional lattice.

    Citation: Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata. Dynamics of an ultra-discrete SIR epidemic model with time delay[J]. Mathematical Biosciences and Engineering, 2018, 15(3): 653-666. doi: 10.3934/mbe.2018029

    Related Papers:

  • We propose an ultra-discretization for an SIR epidemic model with time delay. It is proven that the ultra-discrete model has a threshold property concerning global attractivity of equilibria as shown in differential and difference equation models. We also study an interesting convergence pattern of the solution, which is illustrated in a two-dimensional lattice.


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