Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models
We present a constructive method for Lyapunov functions forordinary differential equation models of infectious diseases in vivo.We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using thoseof simpler models. Especially, we construct Lyapuno...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.117 |
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| _version_ | 1832590101921660928 |
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| author | Tsuyoshi Kajiwara Toru Sasaki Yasuhiro Takeuchi |
| author_facet | Tsuyoshi Kajiwara Toru Sasaki Yasuhiro Takeuchi |
| author_sort | Tsuyoshi Kajiwara |
| collection | DOAJ |
| description | We present a constructive method for Lyapunov functions forordinary differential equation models of infectious diseases in vivo.We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using thoseof simpler models. Especially, we construct Lyapunov functions for modelswith an immune variable from those for models without an immunevariable, a Lyapunov functions of a model with absorption effectfrom that for a model without absorption effect. We make theconstruction clear for Lyapunov functions proposed previously, andpresent new results with our method. |
| format | Article |
| id | doaj-art-1f676460a3674cb6a157fbe81186eab4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1f676460a3674cb6a157fbe81186eab42025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112111713310.3934/mbe.2015.12.117Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex modelsTsuyoshi Kajiwara0Toru Sasaki1Yasuhiro Takeuchi2Graduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, OkayamaGraduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, OkayamaCollege of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, SagamiharaWe present a constructive method for Lyapunov functions forordinary differential equation models of infectious diseases in vivo.We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using thoseof simpler models. Especially, we construct Lyapunov functions for modelswith an immune variable from those for models without an immunevariable, a Lyapunov functions of a model with absorption effectfrom that for a model without absorption effect. We make theconstruction clear for Lyapunov functions proposed previously, andpresent new results with our method.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.117stabilitylyapunov functionsimmunity.ordinary differential equationsinfectious diseases |
| spellingShingle | Tsuyoshi Kajiwara Toru Sasaki Yasuhiro Takeuchi Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models Mathematical Biosciences and Engineering stability lyapunov functions immunity. ordinary differential equations infectious diseases |
| title | Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models |
| title_full | Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models |
| title_fullStr | Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models |
| title_full_unstemmed | Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models |
| title_short | Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models |
| title_sort | construction of lyapunov functions for some models of infectious diseases in vivo from simple models to complex models |
| topic | stability lyapunov functions immunity. ordinary differential equations infectious diseases |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.117 |
| work_keys_str_mv | AT tsuyoshikajiwara constructionoflyapunovfunctionsforsomemodelsofinfectiousdiseasesinvivofromsimplemodelstocomplexmodels AT torusasaki constructionoflyapunovfunctionsforsomemodelsofinfectiousdiseasesinvivofromsimplemodelstocomplexmodels AT yasuhirotakeuchi constructionoflyapunovfunctionsforsomemodelsofinfectiousdiseasesinvivofromsimplemodelstocomplexmodels |