Dynamics Analysis of a Stochastic SIR Epidemic Model
We investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively. By constructing suitable Lyapunov functions and applyin...
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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/10.1155/2014/356013 |
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| _version_ | 1832568214638297088 |
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| author | Feng Rao |
| author_facet | Feng Rao |
| author_sort | Feng Rao |
| collection | DOAJ |
| description | We investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively. By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence. A series of numerical simulations to illustrate these mathematical findings are presented. |
| format | Article |
| id | doaj-art-5907cf7f367d45d9a8e71a948e7755fa |
| 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-5907cf7f367d45d9a8e71a948e7755fa2025-02-03T00:59:28ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/356013356013Dynamics Analysis of a Stochastic SIR Epidemic ModelFeng Rao0College of Sciences, Nanjing University of Technology, Nanjing 211816, ChinaWe investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively. By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence. A series of numerical simulations to illustrate these mathematical findings are presented.http://dx.doi.org/10.1155/2014/356013 |
| spellingShingle | Feng Rao Dynamics Analysis of a Stochastic SIR Epidemic Model Abstract and Applied Analysis |
| title | Dynamics Analysis of a Stochastic SIR Epidemic Model |
| title_full | Dynamics Analysis of a Stochastic SIR Epidemic Model |
| title_fullStr | Dynamics Analysis of a Stochastic SIR Epidemic Model |
| title_full_unstemmed | Dynamics Analysis of a Stochastic SIR Epidemic Model |
| title_short | Dynamics Analysis of a Stochastic SIR Epidemic Model |
| title_sort | dynamics analysis of a stochastic sir epidemic model |
| url | http://dx.doi.org/10.1155/2014/356013 |
| work_keys_str_mv | AT fengrao dynamicsanalysisofastochasticsirepidemicmodel |