Sveir epidemiological model with varying infectivity and distributed delays
In this paper, based on an SEIR epidemiologicalmodel with distributed delays to account for varying infectivity, weintroduce a vaccination compartment, leading to an SVEIR model. Byemploying direct Lyapunov method and LaSalle's invariance principle,we construct appropriate functionals that inte...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.875 |
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| author | Jinliang Wang Gang Huang Yasuhiro Takeuchi Shengqiang Liu |
| author_facet | Jinliang Wang Gang Huang Yasuhiro Takeuchi Shengqiang Liu |
| author_sort | Jinliang Wang |
| collection | DOAJ |
| description | In this paper, based on an SEIR epidemiologicalmodel with distributed delays to account for varying infectivity, weintroduce a vaccination compartment, leading to an SVEIR model. Byemploying direct Lyapunov method and LaSalle's invariance principle,we construct appropriate functionals that integrate over past statesto establish global asymptotic stability conditions, which arecompletely determined by the basic reproduction number$\mathcal{R}_0^V$. More precisely, it is shown that, if$\mathcal{R}_0^V\leq 1$, then the disease free equilibrium isglobally asymptotically stable; if $\mathcal{R}_0^V> 1$, then there exists a unique endemic equilibrium which isglobally asymptotically stable. Mathematicalresults suggest that vaccination is helpful for disease control bydecreasing the basic reproduction number. However, there is anecessary condition for successful elimination of disease. If thetime for the vaccinees to obtain immunity or the possibility forthem to be infected before acquiring immunity can be neglected, thiscondition would be satisfied and the disease can always be eradicatedby some suitable vaccination strategies. This may lead toover-evaluating the effect of vaccination. |
| format | Article |
| id | doaj-art-4aef6fa7c80c4b59ac331ff3fd3c3d9c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4aef6fa7c80c4b59ac331ff3fd3c3d9c2025-01-24T02:02:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-05-018387588810.3934/mbe.2011.8.875Sveir epidemiological model with varying infectivity and distributed delaysJinliang Wang0Gang Huang1Yasuhiro Takeuchi2Shengqiang Liu3Department of Mathematics, Harbin Institute of Technology, Harbin 150001Department of Mathematics, Harbin Institute of Technology, Harbin 150001Department of Mathematics, Harbin Institute of Technology, Harbin 150001Department of Mathematics, Harbin Institute of Technology, Harbin 150001In this paper, based on an SEIR epidemiologicalmodel with distributed delays to account for varying infectivity, weintroduce a vaccination compartment, leading to an SVEIR model. Byemploying direct Lyapunov method and LaSalle's invariance principle,we construct appropriate functionals that integrate over past statesto establish global asymptotic stability conditions, which arecompletely determined by the basic reproduction number$\mathcal{R}_0^V$. More precisely, it is shown that, if$\mathcal{R}_0^V\leq 1$, then the disease free equilibrium isglobally asymptotically stable; if $\mathcal{R}_0^V> 1$, then there exists a unique endemic equilibrium which isglobally asymptotically stable. Mathematicalresults suggest that vaccination is helpful for disease control bydecreasing the basic reproduction number. However, there is anecessary condition for successful elimination of disease. If thetime for the vaccinees to obtain immunity or the possibility forthem to be infected before acquiring immunity can be neglected, thiscondition would be satisfied and the disease can always be eradicatedby some suitable vaccination strategies. This may lead toover-evaluating the effect of vaccination.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.875global stability.vaccination strategydistributed delaysvaryinginfectivityepidemic model |
| spellingShingle | Jinliang Wang Gang Huang Yasuhiro Takeuchi Shengqiang Liu Sveir epidemiological model with varying infectivity and distributed delays Mathematical Biosciences and Engineering global stability. vaccination strategy distributed delays varyinginfectivity epidemic model |
| title | Sveir epidemiological model with varying infectivity and distributed delays |
| title_full | Sveir epidemiological model with varying infectivity and distributed delays |
| title_fullStr | Sveir epidemiological model with varying infectivity and distributed delays |
| title_full_unstemmed | Sveir epidemiological model with varying infectivity and distributed delays |
| title_short | Sveir epidemiological model with varying infectivity and distributed delays |
| title_sort | sveir epidemiological model with varying infectivity and distributed delays |
| topic | global stability. vaccination strategy distributed delays varyinginfectivity epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.875 |
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