Dynamics of an ultra-discrete SIR epidemic model with time delay
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018029 |
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| author | Masaki Sekiguchi Emiko Ishiwata Yukihiko Nakata |
| author_facet | Masaki Sekiguchi Emiko Ishiwata Yukihiko Nakata |
| author_sort | Masaki Sekiguchi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c3cd02d49df445ddb3c4c9e5081acba1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c3cd02d49df445ddb3c4c9e5081acba12025-01-24T02:40:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-05-0115365366610.3934/mbe.2018029Dynamics of an ultra-discrete SIR epidemic model with time delayMasaki Sekiguchi0Emiko Ishiwata1Yukihiko Nakata2Tokyo Metropolitan Ogikubo High School, 5-7-20, Ogikubo, Suginami-ku, Tokyo 167-0051, JapanDepartment of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, JapanDepartment of Mathematics, Shimane University, 1600 Nishikawatsu-cho, 690-8504, Matsue, JapanWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018029epidemic modelultra-discretizationtime delaydynamics |
| spellingShingle | Masaki Sekiguchi Emiko Ishiwata Yukihiko Nakata Dynamics of an ultra-discrete SIR epidemic model with time delay Mathematical Biosciences and Engineering epidemic model ultra-discretization time delay dynamics |
| title | Dynamics of an ultra-discrete SIR epidemic model with time delay |
| title_full | Dynamics of an ultra-discrete SIR epidemic model with time delay |
| title_fullStr | Dynamics of an ultra-discrete SIR epidemic model with time delay |
| title_full_unstemmed | Dynamics of an ultra-discrete SIR epidemic model with time delay |
| title_short | Dynamics of an ultra-discrete SIR epidemic model with time delay |
| title_sort | dynamics of an ultra discrete sir epidemic model with time delay |
| topic | epidemic model ultra-discretization time delay dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018029 |
| work_keys_str_mv | AT masakisekiguchi dynamicsofanultradiscretesirepidemicmodelwithtimedelay AT emikoishiwata dynamicsofanultradiscretesirepidemicmodelwithtimedelay AT yukihikonakata dynamicsofanultradiscretesirepidemicmodelwithtimedelay |