The Behavior of an SVIR Epidemic Model with Stochastic Perturbation
We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R0. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤ 1 and the perturbation is small, which means that the...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/742730 |
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| _version_ | 1832548624539582464 |
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| author | Yanan Zhao Daqing Jiang |
| author_facet | Yanan Zhao Daqing Jiang |
| author_sort | Yanan Zhao |
| collection | DOAJ |
| description | We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R0. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤ 1 and the perturbation is small, which means that the disease will die out. When R0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions. |
| format | Article |
| id | doaj-art-a279d909fce045f3bedcc40e863ea66b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a279d909fce045f3bedcc40e863ea66b2025-02-03T06:13:29ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/742730742730The Behavior of an SVIR Epidemic Model with Stochastic PerturbationYanan Zhao0Daqing Jiang1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaWe discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R0. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤ 1 and the perturbation is small, which means that the disease will die out. When R0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.http://dx.doi.org/10.1155/2014/742730 |
| spellingShingle | Yanan Zhao Daqing Jiang The Behavior of an SVIR Epidemic Model with Stochastic Perturbation Abstract and Applied Analysis |
| title | The Behavior of an SVIR Epidemic Model with Stochastic Perturbation |
| title_full | The Behavior of an SVIR Epidemic Model with Stochastic Perturbation |
| title_fullStr | The Behavior of an SVIR Epidemic Model with Stochastic Perturbation |
| title_full_unstemmed | The Behavior of an SVIR Epidemic Model with Stochastic Perturbation |
| title_short | The Behavior of an SVIR Epidemic Model with Stochastic Perturbation |
| title_sort | behavior of an svir epidemic model with stochastic perturbation |
| url | http://dx.doi.org/10.1155/2014/742730 |
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