Positive Periodic Solutions of an Epidemic Model with Seasonality
An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number Rd is obtained. Moreover, only the basic r...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/470646 |
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| _version_ | 1832568404563722240 |
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| author | Gui-Quan Sun Zhenguo Bai Zi-Ke Zhang Tao Zhou Zhen Jin |
| author_facet | Gui-Quan Sun Zhenguo Bai Zi-Ke Zhang Tao Zhou Zhen Jin |
| author_sort | Gui-Quan Sun |
| collection | DOAJ |
| description | An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number Rd is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs additional condition Rd>R1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number. |
| format | Article |
| id | doaj-art-06ff66bd47074939ad0e9fa6bf0c0c69 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-06ff66bd47074939ad0e9fa6bf0c0c692025-02-03T00:59:05ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/470646470646Positive Periodic Solutions of an Epidemic Model with SeasonalityGui-Quan Sun0Zhenguo Bai1Zi-Ke Zhang2Tao Zhou3Zhen Jin4Complex Sciences Center, Shanxi University, Taiyuan 030006, ChinaDepartment of Applied Mathematics, Xidian University, Xi’an, Shaanxi 710071, ChinaInstitute of Information Economy, Hangzhou Normal University, Hangzhou 310036, ChinaWeb Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaComplex Sciences Center, Shanxi University, Taiyuan 030006, ChinaAn SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number Rd is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs additional condition Rd>R1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.http://dx.doi.org/10.1155/2013/470646 |
| spellingShingle | Gui-Quan Sun Zhenguo Bai Zi-Ke Zhang Tao Zhou Zhen Jin Positive Periodic Solutions of an Epidemic Model with Seasonality The Scientific World Journal |
| title | Positive Periodic Solutions of an Epidemic Model with Seasonality |
| title_full | Positive Periodic Solutions of an Epidemic Model with Seasonality |
| title_fullStr | Positive Periodic Solutions of an Epidemic Model with Seasonality |
| title_full_unstemmed | Positive Periodic Solutions of an Epidemic Model with Seasonality |
| title_short | Positive Periodic Solutions of an Epidemic Model with Seasonality |
| title_sort | positive periodic solutions of an epidemic model with seasonality |
| url | http://dx.doi.org/10.1155/2013/470646 |
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