Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity
SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/848623 |
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| _version_ | 1832567987497861120 |
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| author | Wencai Zhao Juan Li Xinzhu Meng |
| author_facet | Wencai Zhao Juan Li Xinzhu Meng |
| author_sort | Wencai Zhao |
| collection | DOAJ |
| description | SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. Lastly, some simulations are given to validate the theoretical results. |
| format | Article |
| id | doaj-art-2cf83ac97d1d4f3a87a14e3b8f6c74bf |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2cf83ac97d1d4f3a87a14e3b8f6c74bf2025-02-03T00:59:53ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/848623848623Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong ImmunityWencai Zhao0Juan Li1Xinzhu Meng2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaSIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. Lastly, some simulations are given to validate the theoretical results.http://dx.doi.org/10.1155/2015/848623 |
| spellingShingle | Wencai Zhao Juan Li Xinzhu Meng Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity Discrete Dynamics in Nature and Society |
| title | Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity |
| title_full | Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity |
| title_fullStr | Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity |
| title_full_unstemmed | Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity |
| title_short | Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity |
| title_sort | dynamical analysis of sir epidemic model with nonlinear pulse vaccination and lifelong immunity |
| url | http://dx.doi.org/10.1155/2015/848623 |
| work_keys_str_mv | AT wencaizhao dynamicalanalysisofsirepidemicmodelwithnonlinearpulsevaccinationandlifelongimmunity AT juanli dynamicalanalysisofsirepidemicmodelwithnonlinearpulsevaccinationandlifelongimmunity AT xinzhumeng dynamicalanalysisofsirepidemicmodelwithnonlinearpulsevaccinationandlifelongimmunity |