Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is b...
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| Language: | English |
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AIMS Press
2017-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017033 |
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| author | Kazuo Yamazaki Xueying Wang |
| author_facet | Kazuo Yamazaki Xueying Wang |
| author_sort | Kazuo Yamazaki |
| collection | DOAJ |
| description | We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state. |
| format | Article |
| id | doaj-art-2719d7b716f343d7b27071df78a01ca9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2719d7b716f343d7b27071df78a01ca92025-01-24T02:39:38ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-03-0114255957910.3934/mbe.2017033Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic modelKazuo Yamazaki0Xueying Wang1Department of Mathematics, University of Rochester, Rochester, NY 14627, USADepartment of Mathematics and Statistics, Washington State University, Pullman, WA 99164-3113, USAWe study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state.https://www.aimspress.com/article/doi/10.3934/mbe.2017033basic reproduction numbercholera dynamicspersistenceprincipal eigenvaluesstability |
| spellingShingle | Kazuo Yamazaki Xueying Wang Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model Mathematical Biosciences and Engineering basic reproduction number cholera dynamics persistence principal eigenvalues stability |
| title | Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model |
| title_full | Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model |
| title_fullStr | Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model |
| title_full_unstemmed | Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model |
| title_short | Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model |
| title_sort | global stability and uniform persistence of the reaction convection diffusion cholera epidemic model |
| topic | basic reproduction number cholera dynamics persistence principal eigenvalues stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017033 |
| work_keys_str_mv | AT kazuoyamazaki globalstabilityanduniformpersistenceofthereactionconvectiondiffusioncholeraepidemicmodel AT xueyingwang globalstabilityanduniformpersistenceofthereactionconvectiondiffusioncholeraepidemicmodel |