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Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19

Author

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  • Abbasi, Zohreh
  • Zamani, Iman
  • Mehra, Amir Hossein Amiri
  • Shafieirad, Mohsen
  • Ibeas, Asier

Abstract

This paper presents a SEIAR-type model considering quarantined individuals (Q), called SQEIAR model. The dynamic of SQEIAR model is defined by six ordinary differential equations that describe the numbers of Susceptible, Quarantined, Exposed, Infected, Asymptomatic, and Recovered individuals. The goal of this paper is to reduce the size of susceptible, infected, exposed and asymptomatic groups to consequently eradicate the infection by using two actions: the quarantine and the treatment of infected people. To reach this purpose, optimal control theory is presented to control the epidemic model over free terminal optimal time control with an optimal cost. Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. Also, an impulsive epidemic model of SQEIAR is considered to deal with the potential suddenly increased in population caused by immigration or travel. Since this model is suitable to describe the COVID-19 pandemic, especial attention is devoted to this case. Thus, numerical simulations are given to prove the accuracy of the theoretical claims and applied to the particular data of this infection. Moreover, numerical computations of the COVID-19 are compared with diseases like Ebola and Influenza. In addition, the controller is evaluated with system parameters identified by using actual data of China. Finally, the controller tuned with the estimated parameters of the Chinese data is applied to the actual data of Spain to compare the quarantine and treatment policies in both countries.

Suggested Citation

  • Abbasi, Zohreh & Zamani, Iman & Mehra, Amir Hossein Amiri & Shafieirad, Mohsen & Ibeas, Asier, 2020. "Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304513
    DOI: 10.1016/j.chaos.2020.110054
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    References listed on IDEAS

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    1. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
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    Cited by:

    1. Utsumi, Shinobu & Arefin, Md. Rajib & Tatsukawa, Yuichi & Tanimoto, Jun, 2022. "How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Masoud Saade & Sebastian AniĊ£a & Vitaly Volpert, 2023. "Dynamics of Persistent Epidemic and Optimal Control of Vaccination," Mathematics, MDPI, vol. 11(17), pages 1-15, September.
    3. Manuel De la Sen & Santiago Alonso-Quesada & Asier Ibeas, 2021. "On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility," Mathematics, MDPI, vol. 9(5), pages 1-32, March.
    4. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    6. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Mirzaee, Alireza & Dehghani, Maryam & Mohammadi, Mohsen, 2021. "Optimal impulsive blood glucose control through multiple injections," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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