Threshold dynamics of a stochastic general SIRS epidemic model with migration
In this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023497?viewType=HTML |
| _version_ | 1797822217417916416 |
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| author | Zhongwei Cao Jian Zhang Huishuang Su Li Zu |
| author_facet | Zhongwei Cao Jian Zhang Huishuang Su Li Zu |
| author_sort | Zhongwei Cao |
| collection | DOAJ |
| description | In this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will become extinct with certainty, given additional conditions. Conversely, if $ R_0^S > 1 $, the disease has the potential to persist. Moreover, the necessary conditions for the existence of the stationary distribution of positive solution in the event of disease persistence is determined. Our theoretical findings are validated through numerical simulations. |
| first_indexed | 2024-03-13T10:04:43Z |
| format | Article |
| id | doaj.art-c976bf0298464716b52e4dfc4292100f |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-13T10:04:43Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-c976bf0298464716b52e4dfc4292100f2023-05-23T01:23:10ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-04-01206112121123710.3934/mbe.2023497Threshold dynamics of a stochastic general SIRS epidemic model with migrationZhongwei Cao0Jian Zhang 1Huishuang Su2Li Zu 31. Logistics Industry Economy and Intelligent Logistics Laboratory, Jilin University of Finance and Economics, Changchun 130117, China2. Department of Basic Teaching and Research, Changchun Finance College, Changchun 130028, China3. Yatai School of Business Management, Jilin University of Finance and Economics, Changchun 130117, China4. College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, ChinaIn this study, a stochastic SIRS epidemic model that features constant immigration and general incidence rate is investigated. Our findings show that the dynamical behaviors of the stochastic system can be predicted using the stochastic threshold $ R_0^S $. If $ R_0^S < 1 $, the disease will become extinct with certainty, given additional conditions. Conversely, if $ R_0^S > 1 $, the disease has the potential to persist. Moreover, the necessary conditions for the existence of the stationary distribution of positive solution in the event of disease persistence is determined. Our theoretical findings are validated through numerical simulations.https://www.aimspress.com/article/doi/10.3934/mbe.2023497?viewType=HTMLimmigrationgeneral incidence ratesirs epidemic modelthreshold dynamicsergodicity |
| spellingShingle | Zhongwei Cao Jian Zhang Huishuang Su Li Zu Threshold dynamics of a stochastic general SIRS epidemic model with migration Mathematical Biosciences and Engineering immigration general incidence rate sirs epidemic model threshold dynamics ergodicity |
| title | Threshold dynamics of a stochastic general SIRS epidemic model with migration |
| title_full | Threshold dynamics of a stochastic general SIRS epidemic model with migration |
| title_fullStr | Threshold dynamics of a stochastic general SIRS epidemic model with migration |
| title_full_unstemmed | Threshold dynamics of a stochastic general SIRS epidemic model with migration |
| title_short | Threshold dynamics of a stochastic general SIRS epidemic model with migration |
| title_sort | threshold dynamics of a stochastic general sirs epidemic model with migration |
| topic | immigration general incidence rate sirs epidemic model threshold dynamics ergodicity |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023497?viewType=HTML |
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