A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation
We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prov...
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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/10.1155/2013/792308 |
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| _version_ | 1832548161161265152 |
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| author | Wenbin Liu |
| author_facet | Wenbin Liu |
| author_sort | Wenbin Liu |
| collection | DOAJ |
| description | We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium. |
| format | Article |
| id | doaj-art-eff5b4e9682945f3a298144cef4f6c5c |
| 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-eff5b4e9682945f3a298144cef4f6c5c2025-02-03T06:42:13ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/792308792308A SIRS Epidemic Model Incorporating Media Coverage with Random PerturbationWenbin Liu0College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, ChinaWe investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium.http://dx.doi.org/10.1155/2013/792308 |
| spellingShingle | Wenbin Liu A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation Abstract and Applied Analysis |
| title | A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation |
| title_full | A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation |
| title_fullStr | A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation |
| title_full_unstemmed | A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation |
| title_short | A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation |
| title_sort | sirs epidemic model incorporating media coverage with random perturbation |
| url | http://dx.doi.org/10.1155/2013/792308 |
| work_keys_str_mv | AT wenbinliu asirsepidemicmodelincorporatingmediacoveragewithrandomperturbation AT wenbinliu sirsepidemicmodelincorporatingmediacoveragewithrandomperturbation |