The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence
An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗<1. The infection-free periodic sol...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/490437 |
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| _version_ | 1832560466867519488 |
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| author | Juping Zhang Zhen Jin Yakui Xue Youwen Li |
| author_facet | Juping Zhang Zhen Jin Yakui Xue Youwen Li |
| author_sort | Juping Zhang |
| collection | DOAJ |
| description | An SIR epidemic model with pulse birth and
standard incidence is presented. The dynamics of the epidemic model
is analyzed. The basic reproductive number R∗ is defined. It is
proved that the infection-free periodic solution is global asymptotically stable if R∗<1. The infection-free periodic
solution is unstable and the disease is uniform persistent if R∗>1. Our theoretical results are confirmed by numerical simulations. |
| format | Article |
| id | doaj-art-151f64c12cd44bc99422e83fc50e7277 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-151f64c12cd44bc99422e83fc50e72772025-02-03T01:27:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/490437490437The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard IncidenceJuping Zhang0Zhen Jin1Yakui Xue2Youwen Li3Department of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, School of Science, North University of China, Taiyuan, Shanxi 030051, ChinaAn SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗<1. The infection-free periodic solution is unstable and the disease is uniform persistent if R∗>1. Our theoretical results are confirmed by numerical simulations.http://dx.doi.org/10.1155/2009/490437 |
| spellingShingle | Juping Zhang Zhen Jin Yakui Xue Youwen Li The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence Discrete Dynamics in Nature and Society |
| title | The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence |
| title_full | The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence |
| title_fullStr | The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence |
| title_full_unstemmed | The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence |
| title_short | The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence |
| title_sort | dynamics of the pulse birth in an sir epidemic model with standard incidence |
| url | http://dx.doi.org/10.1155/2009/490437 |
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