| Stochastic optimal control for norovirus transmission dynamics by contaminated food and water |
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| 作者姓名： | Anwarud Din 黎永锦 |
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| 作者单位： | Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China |
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| 基金项目： | supported by the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(Grant No.34000-31610293)。 |
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| 摘 要： | Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.
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| 关 键 词： | stochastic norovirus model stochastic transmission stochastic perturbation stochastic stability stochastic optimal control |
| 收稿时间： | 2021-06-24 |
Stochastic optimal control for norovirus transmission dynamics by contaminated food and water |
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| Anwarud Din,Yongjin Li.Stochastic optimal control for norovirus transmission dynamics by contaminated food and water[J].Chinese Physics B,2022,31(2):20202-020202. |
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| Authors: | Anwarud Din Yongjin Li |
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| Affiliation: | Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China |
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| Abstract: | Norovirus is one of the most common causes of viral gastroenteritis in the world, causing significant morbidity, deaths, and medical costs. In this work, we look at stochastic modelling methodologies for norovirus transmission by water, human to human transmission and food. To begin, the proposed stochastic model is shown to have a single global positive solution. Second, we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution $\mathfrak{R_s^0}>1$ by developing a Lyapunov function. Thirdly, we find sufficient criteria $\mathfrak{R_s}<1$ for disease extinction. Finally, two simulation examples are used to exemplify the analytical results. We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures. Additional graphical solutions have been produced to further verify the acquired analytical results. This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world. Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances. |
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| Keywords: | stochastic norovirus model stochastic transmission stochastic perturbation stochastic stability stochastic optimal control |
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