The Global Behavior of a Periodic Epidemic Model with Travel between Patches
We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio R0 and...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/295060 |
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| _version_ | 1850237935055536128 |
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| author | Luosheng Wen Bin Long Xin Liang Fengling Zeng |
| author_facet | Luosheng Wen Bin Long Xin Liang Fengling Zeng |
| author_sort | Luosheng Wen |
| collection | DOAJ |
| description | We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio R0 and two theorems on the global behavior: if R0 < 1 the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then it is unstable; if R0 > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results. |
| format | Article |
| id | doaj-art-07fca09d4bfc42448fb84408497ee45e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-07fca09d4bfc42448fb84408497ee45e2025-08-20T02:01:39ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/295060295060The Global Behavior of a Periodic Epidemic Model with Travel between PatchesLuosheng Wen0Bin Long1Xin Liang2Fengling Zeng3School of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaWe establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio R0 and two theorems on the global behavior: if R0 < 1 the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then it is unstable; if R0 > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.http://dx.doi.org/10.1155/2012/295060 |
| spellingShingle | Luosheng Wen Bin Long Xin Liang Fengling Zeng The Global Behavior of a Periodic Epidemic Model with Travel between Patches Abstract and Applied Analysis |
| title | The Global Behavior of a Periodic Epidemic Model with Travel between Patches |
| title_full | The Global Behavior of a Periodic Epidemic Model with Travel between Patches |
| title_fullStr | The Global Behavior of a Periodic Epidemic Model with Travel between Patches |
| title_full_unstemmed | The Global Behavior of a Periodic Epidemic Model with Travel between Patches |
| title_short | The Global Behavior of a Periodic Epidemic Model with Travel between Patches |
| title_sort | global behavior of a periodic epidemic model with travel between patches |
| url | http://dx.doi.org/10.1155/2012/295060 |
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