The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence
The threshold of a stochastic SIRS model with vertical transmission and saturated incidence is investigated. If the noise is small, it is shown that the threshold of the stochastic system determines the extinction and persistence of the epidemic. In addition, we find that if the noise is large, the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/5620301 |
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| _version_ | 1832553539769991168 |
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| author | Chunjuan Zhu Guangzhao Zeng Yufeng Sun |
| author_facet | Chunjuan Zhu Guangzhao Zeng Yufeng Sun |
| author_sort | Chunjuan Zhu |
| collection | DOAJ |
| description | The threshold of a stochastic SIRS model with vertical transmission and saturated incidence is investigated. If the noise is small, it is shown that the threshold of the stochastic system determines the extinction and persistence of the epidemic. In addition, we find that if the noise is large, the epidemic still prevails. Finally, numerical simulations are given to illustrate the results. |
| format | Article |
| id | doaj-art-48b96b93ce244ac5874948f3a98994d4 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-48b96b93ce244ac5874948f3a98994d42025-02-03T05:53:45ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/56203015620301The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated IncidenceChunjuan Zhu0Guangzhao Zeng1Yufeng Sun2School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, ChinaSchool of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, ChinaSchool of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, ChinaThe threshold of a stochastic SIRS model with vertical transmission and saturated incidence is investigated. If the noise is small, it is shown that the threshold of the stochastic system determines the extinction and persistence of the epidemic. In addition, we find that if the noise is large, the epidemic still prevails. Finally, numerical simulations are given to illustrate the results.http://dx.doi.org/10.1155/2017/5620301 |
| spellingShingle | Chunjuan Zhu Guangzhao Zeng Yufeng Sun The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence Discrete Dynamics in Nature and Society |
| title | The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence |
| title_full | The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence |
| title_fullStr | The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence |
| title_full_unstemmed | The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence |
| title_short | The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence |
| title_sort | threshold of a stochastic sirs model with vertical transmission and saturated incidence |
| url | http://dx.doi.org/10.1155/2017/5620301 |
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