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

Masaki Sekiguchi; Emiko Ishiwata; Yukihiko Nakata

doi:10.3934/mbe.2018029

Mathematical Biosciences and Engineering, 2018, 15(3): 653-666. doi: 10.3934/mbe.2018029.

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

Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata

1. Tokyo Metropolitan Ogikubo High School, 5-7-20, Ogikubo, Suginami-ku, Tokyo 167-0051, Japan
2. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
3. Department of Mathematics, Shimane University, 1600 Nishikawatsu-cho, 690-8504, Matsue, Japan

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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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Keywords: Epidemic model; ultra-discretization; time delay; dynamics

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

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