Markovian switching for near-optimal control of a stochastic SIV epidemic model
As it is known that environmental perturbation is a key component of epidemic models, and Markov process reveals how the noise affects epidemic systems. The paper introduces Markov chain into a stochastic susceptible-infected-vaccination(SIV) epidemic model composed of vaccination and saturated trea...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2019066?viewType=HTML |
| _version_ | 1828891053958103040 |
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| author | ZongWang Qimin Zhang Xining Li |
| author_facet | ZongWang Qimin Zhang Xining Li |
| author_sort | ZongWang |
| collection | DOAJ |
| description | As it is known that environmental perturbation is a key component of epidemic models, and Markov process reveals how the noise affects epidemic systems. The paper introduces Markov chain into a stochastic susceptible-infected-vaccination(SIV) epidemic model composed of vaccination and saturated treatment to analyze the near-optimal control. Based on Pontryagin stochastic maximum principle, the paper gives adequate and all necessary conditions for near-optimal control. Numerical simulations are presented to display the theoretical results and verify the effect of treatment control on epidemic diseases. |
| first_indexed | 2024-12-13T13:11:16Z |
| format | Article |
| id | doaj.art-cc5be39362e5420c88f97014ff2b883e |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-13T13:11:16Z |
| publishDate | 2019-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-cc5be39362e5420c88f97014ff2b883e2022-12-21T23:44:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-02-011631348137510.3934/mbe.2019066Markovian switching for near-optimal control of a stochastic SIV epidemic modelZongWang0Qimin Zhang1Xining Li21. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, P.R. China1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, P.R. China 2. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, P.R. China 2. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. ChinaAs it is known that environmental perturbation is a key component of epidemic models, and Markov process reveals how the noise affects epidemic systems. The paper introduces Markov chain into a stochastic susceptible-infected-vaccination(SIV) epidemic model composed of vaccination and saturated treatment to analyze the near-optimal control. Based on Pontryagin stochastic maximum principle, the paper gives adequate and all necessary conditions for near-optimal control. Numerical simulations are presented to display the theoretical results and verify the effect of treatment control on epidemic diseases.https://www.aimspress.com/article/doi/10.3934/mbe.2019066?viewType=HTMLsiv epidemic modelmarkov chainnear-optimal controlhamiltonian functionsufficient and necessary conditions |
| spellingShingle | ZongWang Qimin Zhang Xining Li Markovian switching for near-optimal control of a stochastic SIV epidemic model Mathematical Biosciences and Engineering siv epidemic model markov chain near-optimal control hamiltonian function sufficient and necessary conditions |
| title | Markovian switching for near-optimal control of a stochastic SIV epidemic model |
| title_full | Markovian switching for near-optimal control of a stochastic SIV epidemic model |
| title_fullStr | Markovian switching for near-optimal control of a stochastic SIV epidemic model |
| title_full_unstemmed | Markovian switching for near-optimal control of a stochastic SIV epidemic model |
| title_short | Markovian switching for near-optimal control of a stochastic SIV epidemic model |
| title_sort | markovian switching for near optimal control of a stochastic siv epidemic model |
| topic | siv epidemic model markov chain near-optimal control hamiltonian function sufficient and necessary conditions |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2019066?viewType=HTML |
| work_keys_str_mv | AT zongwang markovianswitchingfornearoptimalcontrolofastochasticsivepidemicmodel AT qiminzhang markovianswitchingfornearoptimalcontrolofastochasticsivepidemicmodel AT xiningli markovianswitchingfornearoptimalcontrolofastochasticsivepidemicmodel |