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Dynamic analysis and optimal control of a stochastic COVID-19 model

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  • Zhang, Ge
  • Li, Zhiming
  • Din, Anwarud
  • Chen, Tao

Abstract

In this paper, we construct a stochastic SAIR (Susceptible–Asymptomatic–Infected–Removed) epidemic model to study the dynamic and control strategy of COVID-19. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. We prove the necessary conditions for the existence of extinction and ergodic stationary distribution by defining two new thresholds, respectively. Through the stochastic control theory, the optimal control strategy is obtained. Numerical simulations show the validity of stationary distribution and optimal control. The parameters of the model are estimated by a set of real COVID-19 data. And, the sensitivity of all parameters shows that decreasing physical interaction and screening the asymptomatic as swiftly as possible can prevent the wide spread of the virus in communities. Finally, we also display the trend of the epidemic without control strategies.

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  • Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
  • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:498-517
    DOI: 10.1016/j.matcom.2023.08.005
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    References listed on IDEAS

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    1. Su, Tan & Yang, Qing & Zhang, Xinhong & Jiang, Daqing, 2023. "Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    2. H. J. Alsakaji & F. A. Rihan & A. Hashish & Georgi Georgiev, 2022. "Dynamics of a Stochastic Epidemic Model with Vaccination and Multiple Time-Delays for COVID-19 in the UAE," Complexity, Hindawi, vol. 2022, pages 1-15, April.
    3. Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Aldila, Dipo & Khoshnaw, Sarbaz H.A. & Safitri, Egi & Anwar, Yusril Rais & Bakry, Aanisah R.Q. & Samiadji, Brenda M. & Anugerah, Demas A. & GH, M. Farhan Alfarizi & Ayulani, Indri D. & Salim, Sheryl N, 2020. "A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    8. Crokidakis, Nuno, 2020. "COVID-19 spreading in Rio de Janeiro, Brazil: Do the policies of social isolation really work?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Yiheng Li, 2024. "Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters," Mathematics, MDPI, vol. 12(10), pages 1-15, May.
    2. Juhui Yan & Wanqin Wu & Qing Miao & Xuewen Tan, 2024. "Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate," Mathematics, MDPI, vol. 12(17), pages 1-21, September.

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