Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation
We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant distribution which is ergod...
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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/10.1155/2013/917389 |
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| _version_ | 1850168252085305344 |
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| author | Yuguo Lin Daqing Jiang |
| author_facet | Yuguo Lin Daqing Jiang |
| author_sort | Yuguo Lin |
| collection | DOAJ |
| description | We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant
distribution which is ergodic if ℛ0>1. This is the same situation as the corresponding deterministic
case. When the intensity of white noise is large, white noise controls this system. This means that
the disease will extinct exponentially regardless of the magnitude of ℛ0. |
| format | Article |
| id | doaj-art-e14d2fcd2f5f429db449ad812ea37ee4 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e14d2fcd2f5f429db449ad812ea37ee42025-08-20T02:21:01ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/917389917389Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic PerturbationYuguo Lin0Daqing Jiang1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaWe introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant distribution which is ergodic if ℛ0>1. This is the same situation as the corresponding deterministic case. When the intensity of white noise is large, white noise controls this system. This means that the disease will extinct exponentially regardless of the magnitude of ℛ0.http://dx.doi.org/10.1155/2013/917389 |
| spellingShingle | Yuguo Lin Daqing Jiang Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation Abstract and Applied Analysis |
| title | Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation |
| title_full | Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation |
| title_fullStr | Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation |
| title_full_unstemmed | Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation |
| title_short | Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation |
| title_sort | dynamics of a multigroup sir epidemic model with nonlinear incidence and stochastic perturbation |
| url | http://dx.doi.org/10.1155/2013/917389 |
| work_keys_str_mv | AT yuguolin dynamicsofamultigroupsirepidemicmodelwithnonlinearincidenceandstochasticperturbation AT daqingjiang dynamicsofamultigroupsirepidemicmodelwithnonlinearincidenceandstochasticperturbation |