Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment
In this paper, we represented the optimal control and dynamics of a stochastic SEIR epidemic model with nonlinear incidence and treatment rate. By using the Lyapunov function method, the existence and uniqueness of the global positive solution of the model were proved. The dynamic analysis of the st...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241600 |
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| _version_ | 1832590778449264640 |
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| author | Jinji Du Chuangliang Qin Yuanxian Hui |
| author_facet | Jinji Du Chuangliang Qin Yuanxian Hui |
| author_sort | Jinji Du |
| collection | DOAJ |
| description | In this paper, we represented the optimal control and dynamics of a stochastic SEIR epidemic model with nonlinear incidence and treatment rate. By using the Lyapunov function method, the existence and uniqueness of the global positive solution of the model were proved. The dynamic analysis of the stochastic model was studied and we found that the model has an ergodic stationary distribution when $ R_{0}^{s} > 1 $. The disease was extinct when $ R_{0}^{e} < 1 $. The optimal solution of the disease was obtained by using the stochastic control theory. The numerical simulation of our conclusion was carried out. The results showed that the disease decreased with the increase of the control variables. |
| format | Article |
| id | doaj-art-d6896d3496864ce0927caa97df5fd6da |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-d6896d3496864ce0927caa97df5fd6da2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912335323355010.3934/math.20241600Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatmentJinji Du0Chuangliang Qin1Yuanxian Hui2School of Mathematics and Statistics, Xinyang College, Xinyang 464000, ChinaSchool of Mathematics and Statistics, Xinyang College, Xinyang 464000, ChinaSchool of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, ChinaIn this paper, we represented the optimal control and dynamics of a stochastic SEIR epidemic model with nonlinear incidence and treatment rate. By using the Lyapunov function method, the existence and uniqueness of the global positive solution of the model were proved. The dynamic analysis of the stochastic model was studied and we found that the model has an ergodic stationary distribution when $ R_{0}^{s} > 1 $. The disease was extinct when $ R_{0}^{e} < 1 $. The optimal solution of the disease was obtained by using the stochastic control theory. The numerical simulation of our conclusion was carried out. The results showed that the disease decreased with the increase of the control variables.https://www.aimspress.com/article/doi/10.3934/math.20241600stochastic seir modelstationary distributionextinctionstochastic control |
| spellingShingle | Jinji Du Chuangliang Qin Yuanxian Hui Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment AIMS Mathematics stochastic seir model stationary distribution extinction stochastic control |
| title | Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment |
| title_full | Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment |
| title_fullStr | Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment |
| title_full_unstemmed | Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment |
| title_short | Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment |
| title_sort | optimal control and analysis of a stochastic seir epidemic model with nonlinear incidence and treatment |
| topic | stochastic seir model stationary distribution extinction stochastic control |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241600 |
| work_keys_str_mv | AT jinjidu optimalcontrolandanalysisofastochasticseirepidemicmodelwithnonlinearincidenceandtreatment AT chuangliangqin optimalcontrolandanalysisofastochasticseirepidemicmodelwithnonlinearincidenceandtreatment AT yuanxianhui optimalcontrolandanalysisofastochasticseirepidemicmodelwithnonlinearincidenceandtreatment |