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

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

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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This article has been cited by

  • 1. Fernando Córdova-Lepe, Rodrigo Gutiérrez, Karina Vilches-Ponce, Analysis of two discrete forms of the classic continuous SIR epidemiological model, Journal of Difference Equations and Applications, 2019, 1, 10.1080/10236198.2019.1696323

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