Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate
A delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible eq...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/678723 |
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| _version_ | 1850120260201480192 |
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| author | Yongzhen Pei Li Changguo Qianyong Wu Yunfei Lv |
| author_facet | Yongzhen Pei Li Changguo Qianyong Wu Yunfei Lv |
| author_sort | Yongzhen Pei |
| collection | DOAJ |
| description | A delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition about the basic reproduction number. By use of new computational techniques for delay differential equations, we prove that the system is permanent. Our results indicate that the recovery rate and the vaccination rate are two factors for the dynamic behavior of the system. Numerical simulations are carried out to investigate the influence of the key parameters on the spread of the disease, to support the analytical conclusion, and to illustrate possible behavioral scenarios of the model. |
| format | Article |
| id | doaj-art-67b4fbef2d1941eb85f7be25397f2030 |
| 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-67b4fbef2d1941eb85f7be25397f20302025-08-20T02:35:23ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/678723678723Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence RateYongzhen Pei0Li Changguo1Qianyong Wu2Yunfei Lv3School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Basic Science, Military Transportation University, Tianjin 300161, ChinaSchool of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaA delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition about the basic reproduction number. By use of new computational techniques for delay differential equations, we prove that the system is permanent. Our results indicate that the recovery rate and the vaccination rate are two factors for the dynamic behavior of the system. Numerical simulations are carried out to investigate the influence of the key parameters on the spread of the disease, to support the analytical conclusion, and to illustrate possible behavioral scenarios of the model.http://dx.doi.org/10.1155/2014/678723 |
| spellingShingle | Yongzhen Pei Li Changguo Qianyong Wu Yunfei Lv Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate Abstract and Applied Analysis |
| title | Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate |
| title_full | Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate |
| title_fullStr | Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate |
| title_full_unstemmed | Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate |
| title_short | Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate |
| title_sort | successive vaccination and difference in immunity of a delay sir model with a general incidence rate |
| url | http://dx.doi.org/10.1155/2014/678723 |
| work_keys_str_mv | AT yongzhenpei successivevaccinationanddifferenceinimmunityofadelaysirmodelwithageneralincidencerate AT lichangguo successivevaccinationanddifferenceinimmunityofadelaysirmodelwithageneralincidencerate AT qianyongwu successivevaccinationanddifferenceinimmunityofadelaysirmodelwithageneralincidencerate AT yunfeilv successivevaccinationanddifferenceinimmunityofadelaysirmodelwithageneralincidencerate |