Mathematical Analysis of a Cholera Model with Vaccination
We consider a SVR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number ℛv. If ℛv<...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/324767 |
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| author | Jing'an Cui Zhanmin Wu Xueyong Zhou |
| author_facet | Jing'an Cui Zhanmin Wu Xueyong Zhou |
| author_sort | Jing'an Cui |
| collection | DOAJ |
| description | We consider a SVR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number ℛv. If ℛv<1, we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if ℛv>1, the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of ℛv on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community. |
| format | Article |
| id | doaj-art-df7b1b419ca64cddb7c094a1f1ac97d7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-df7b1b419ca64cddb7c094a1f1ac97d72025-02-03T06:42:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/324767324767Mathematical Analysis of a Cholera Model with VaccinationJing'an Cui0Zhanmin Wu1Xueyong Zhou2School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaSchool of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, ChinaCollege of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000, ChinaWe consider a SVR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number ℛv. If ℛv<1, we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if ℛv>1, the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of ℛv on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.http://dx.doi.org/10.1155/2014/324767 |
| spellingShingle | Jing'an Cui Zhanmin Wu Xueyong Zhou Mathematical Analysis of a Cholera Model with Vaccination Journal of Applied Mathematics |
| title | Mathematical Analysis of a Cholera Model with Vaccination |
| title_full | Mathematical Analysis of a Cholera Model with Vaccination |
| title_fullStr | Mathematical Analysis of a Cholera Model with Vaccination |
| title_full_unstemmed | Mathematical Analysis of a Cholera Model with Vaccination |
| title_short | Mathematical Analysis of a Cholera Model with Vaccination |
| title_sort | mathematical analysis of a cholera model with vaccination |
| url | http://dx.doi.org/10.1155/2014/324767 |
| work_keys_str_mv | AT jingancui mathematicalanalysisofacholeramodelwithvaccination AT zhanminwu mathematicalanalysisofacholeramodelwithvaccination AT xueyongzhou mathematicalanalysisofacholeramodelwithvaccination |