Stability and persistence in ODE modelsfor populations with many stages
A model of ordinary differential equations is formulated for populationswhich are structured by many stages. The model is motivated by tickswhich are vectors of infectious diseases, but is general enough to apply to many other species.Our analysis identifies a basic reproduction numberthat acts as a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.661 |
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| _version_ | 1832590103251255296 |
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| author | Guihong Fan Yijun Lou Horst R. Thieme Jianhong Wu |
| author_facet | Guihong Fan Yijun Lou Horst R. Thieme Jianhong Wu |
| author_sort | Guihong Fan |
| collection | DOAJ |
| description | A model of ordinary differential equations is formulated for populationswhich are structured by many stages. The model is motivated by tickswhich are vectors of infectious diseases, but is general enough to apply to many other species.Our analysis identifies a basic reproduction numberthat acts as a threshold between population extinction and persistence.We establish conditions for the existence and uniqueness of nonzeroequilibria and show that their local stability cannot be expected ingeneral. Boundedness of solutions remains an open problem though wegive some sufficient conditions. |
| format | Article |
| id | doaj-art-25204fa97968486789ab6e5521cecf3a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-25204fa97968486789ab6e5521cecf3a2025-01-24T02:32:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-03-0112466168610.3934/mbe.2015.12.661Stability and persistence in ODE modelsfor populations with many stagesGuihong Fan0Yijun Lou1Horst R. Thieme2Jianhong Wu3Department of Mathematics and Philosophy, Columbus State University, Columbus, Georgia 31907Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongDepartment of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804Mathematics and Statistics, York University, and Centre for Disease Modelling, York Institute of Health Research, Toronto, OntarioA model of ordinary differential equations is formulated for populationswhich are structured by many stages. The model is motivated by tickswhich are vectors of infectious diseases, but is general enough to apply to many other species.Our analysis identifies a basic reproduction numberthat acts as a threshold between population extinction and persistence.We establish conditions for the existence and uniqueness of nonzeroequilibria and show that their local stability cannot be expected ingeneral. Boundedness of solutions remains an open problem though wegive some sufficient conditions.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.661persistenceuniquenessextinctionbasic reproduction numberboundednessequilibria (existencelyapunov functionsand stability). |
| spellingShingle | Guihong Fan Yijun Lou Horst R. Thieme Jianhong Wu Stability and persistence in ODE modelsfor populations with many stages Mathematical Biosciences and Engineering persistence uniqueness extinction basic reproduction number boundedness equilibria (existence lyapunov functions and stability). |
| title | Stability and persistence in ODE modelsfor populations with many stages |
| title_full | Stability and persistence in ODE modelsfor populations with many stages |
| title_fullStr | Stability and persistence in ODE modelsfor populations with many stages |
| title_full_unstemmed | Stability and persistence in ODE modelsfor populations with many stages |
| title_short | Stability and persistence in ODE modelsfor populations with many stages |
| title_sort | stability and persistence in ode modelsfor populations with many stages |
| topic | persistence uniqueness extinction basic reproduction number boundedness equilibria (existence lyapunov functions and stability). |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.661 |
| work_keys_str_mv | AT guihongfan stabilityandpersistenceinodemodelsforpopulationswithmanystages AT yijunlou stabilityandpersistenceinodemodelsforpopulationswithmanystages AT horstrthieme stabilityandpersistenceinodemodelsforpopulationswithmanystages AT jianhongwu stabilityandpersistenceinodemodelsforpopulationswithmanystages |