Global stability of an age-structured cholera model
In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE model...
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| Language: | English |
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AIMS Press
2012-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.641 |
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| author | Jianxin Yang Zhipeng Qiu Xue-Zhi Li |
| author_facet | Jianxin Yang Zhipeng Qiu Xue-Zhi Li |
| author_sort | Jianxin Yang |
| collection | DOAJ |
| description | In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE modelcan be reduced to the multi-stage models investigated in theliterature. By using the method of Lyapunov function, we establishedthe dynamical properties of the PDE model, and the results show thatthe global dynamics of the model is completely determined by thebasic reproduction number $\mathcal R_0$: if $\mathcal R_0 < 1$the cholera dies out, and if $\mathcal R_0>1$ the disease will persist at the endemicequilibrium. Then the global results obtained for multi-stage modelsare extended to the general continuous age model. |
| format | Article |
| id | doaj-art-50d461b6a0fc437cbaa9c26721df81e9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-50d461b6a0fc437cbaa9c26721df81e92025-01-24T02:28:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-12-0111364166510.3934/mbe.2014.11.641Global stability of an age-structured cholera modelJianxin Yang0Zhipeng Qiu1Xue-Zhi Li2Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094Department of Mathematics, Xinyang Normal University, Xinyang 464000In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE modelcan be reduced to the multi-stage models investigated in theliterature. By using the method of Lyapunov function, we establishedthe dynamical properties of the PDE model, and the results show thatthe global dynamics of the model is completely determined by thebasic reproduction number $\mathcal R_0$: if $\mathcal R_0 < 1$the cholera dies out, and if $\mathcal R_0>1$ the disease will persist at the endemicequilibrium. Then the global results obtained for multi-stage modelsare extended to the general continuous age model.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.641age of infectionglobal stabilitylyapunov function.cholera |
| spellingShingle | Jianxin Yang Zhipeng Qiu Xue-Zhi Li Global stability of an age-structured cholera model Mathematical Biosciences and Engineering age of infection global stability lyapunov function. cholera |
| title | Global stability of an age-structured cholera model |
| title_full | Global stability of an age-structured cholera model |
| title_fullStr | Global stability of an age-structured cholera model |
| title_full_unstemmed | Global stability of an age-structured cholera model |
| title_short | Global stability of an age-structured cholera model |
| title_sort | global stability of an age structured cholera model |
| topic | age of infection global stability lyapunov function. cholera |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.641 |
| work_keys_str_mv | AT jianxinyang globalstabilityofanagestructuredcholeramodel AT zhipengqiu globalstabilityofanagestructuredcholeramodel AT xuezhili globalstabilityofanagestructuredcholeramodel |