An SIR epidemic model with vaccination in a patchy environment
In this paper, an SIR patch model with vaccination is formulated to investigate the effect of vaccination coverage and the impact of human mobility on the spread of diseases among patches. The control reproduction number $\mathfrak{R}_v$ is derived. It shows that the disease-free equilibrium is un...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017059 |
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| _version_ | 1832590044830892032 |
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| author | Qianqian Cui Zhipeng Qiu Ling Ding |
| author_facet | Qianqian Cui Zhipeng Qiu Ling Ding |
| author_sort | Qianqian Cui |
| collection | DOAJ |
| description | In this paper, an SIR patch model with vaccination is formulated to investigate the effect of vaccination coverage and the impact of human mobility on the spread of diseases among patches. The control reproduction number $\mathfrak{R}_v$ is derived. It shows that the disease-free equilibrium is unique and is globally asymptotically stable if $\mathfrak{R}_v \lt 1$ , and unstable if $\mathfrak{R}_v \gt 1$ . The sufficient condition for the local stability of boundary equilibria and the existence of equilibria are obtained for the case $n=2$ . Numerical simulations indicate that vaccines can control and prevent the outbreak of infectious in all patches while migration may magnify the outbreak size in one patch and shrink the outbreak size in other patch. |
| format | Article |
| id | doaj-art-554bb73fb9b14fa1b3d002949629cbe3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-554bb73fb9b14fa1b3d002949629cbe32025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61141115710.3934/mbe.2017059An SIR epidemic model with vaccination in a patchy environmentQianqian Cui0Zhipeng Qiu1Ling Ding2School of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaIn this paper, an SIR patch model with vaccination is formulated to investigate the effect of vaccination coverage and the impact of human mobility on the spread of diseases among patches. The control reproduction number $\mathfrak{R}_v$ is derived. It shows that the disease-free equilibrium is unique and is globally asymptotically stable if $\mathfrak{R}_v \lt 1$ , and unstable if $\mathfrak{R}_v \gt 1$ . The sufficient condition for the local stability of boundary equilibria and the existence of equilibria are obtained for the case $n=2$ . Numerical simulations indicate that vaccines can control and prevent the outbreak of infectious in all patches while migration may magnify the outbreak size in one patch and shrink the outbreak size in other patch.https://www.aimspress.com/article/doi/10.3934/mbe.2017059sir modelvaccinationpatchy environmenttransmission dynamicsreproduction number |
| spellingShingle | Qianqian Cui Zhipeng Qiu Ling Ding An SIR epidemic model with vaccination in a patchy environment Mathematical Biosciences and Engineering sir model vaccination patchy environment transmission dynamics reproduction number |
| title | An SIR epidemic model with vaccination in a patchy environment |
| title_full | An SIR epidemic model with vaccination in a patchy environment |
| title_fullStr | An SIR epidemic model with vaccination in a patchy environment |
| title_full_unstemmed | An SIR epidemic model with vaccination in a patchy environment |
| title_short | An SIR epidemic model with vaccination in a patchy environment |
| title_sort | sir epidemic model with vaccination in a patchy environment |
| topic | sir model vaccination patchy environment transmission dynamics reproduction number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017059 |
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