Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control
This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic si...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/853960 |
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| _version_ | 1850162506692034560 |
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| author | Xiying Wang Wei Xu Yujun Cui Xiaomei Wang |
| author_facet | Xiying Wang Wei Xu Yujun Cui Xiaomei Wang |
| author_sort | Xiying Wang |
| collection | DOAJ |
| description | This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward. |
| format | Article |
| id | doaj-art-fe5562ed996a46689cc4ce3a4ec0935c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fe5562ed996a46689cc4ce3a4ec0935c2025-08-20T02:22:33ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/853960853960Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse ControlXiying Wang0Wei Xu1Yujun Cui2Xiaomei Wang3Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, ChinaDepartment of Applied Mathematics, Shandong University of Science and Technology, Qingdao, Shandong 266510, ChinaSchool of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaThis paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward.http://dx.doi.org/10.1155/2014/853960 |
| spellingShingle | Xiying Wang Wei Xu Yujun Cui Xiaomei Wang Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control Abstract and Applied Analysis |
| title | Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control |
| title_full | Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control |
| title_fullStr | Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control |
| title_full_unstemmed | Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control |
| title_short | Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control |
| title_sort | mathematical analysis of hiv models with switching nonlinear incidence functions and pulse control |
| url | http://dx.doi.org/10.1155/2014/853960 |
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