Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate
We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/172631 |
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| _version_ | 1832556568601690112 |
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| author | Yongli Cai Xixi Wang Weiming Wang Min Zhao |
| author_facet | Yongli Cai Xixi Wang Weiming Wang Min Zhao |
| author_sort | Yongli Cai |
| collection | DOAJ |
| description | We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles. |
| format | Article |
| id | doaj-art-af9a36843e0942eebc2550df16b32e4f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-af9a36843e0942eebc2550df16b32e4f2025-02-03T05:45:04ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/172631172631Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence RateYongli Cai0Xixi Wang1Weiming Wang2Min Zhao3College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Life and Environmental Science, Wenzhou University, Wenzhou 325035, ChinaWe investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.http://dx.doi.org/10.1155/2013/172631 |
| spellingShingle | Yongli Cai Xixi Wang Weiming Wang Min Zhao Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate Abstract and Applied Analysis |
| title | Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate |
| title_full | Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate |
| title_fullStr | Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate |
| title_full_unstemmed | Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate |
| title_short | Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate |
| title_sort | stochastic dynamics of an sirs epidemic model with ratio dependent incidence rate |
| url | http://dx.doi.org/10.1155/2013/172631 |
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