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Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

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  • Kouidere, Abdelfatah
  • Kada, Driss
  • Balatif, Omar
  • Rachik, Mostafa
  • Naim, Mouhcine

Abstract

As of June 02, 2020. The number of people infected with COVID-19 virus in Brazil was about 529,405, the number of death is 30046, the number of recovered is 211080, and the number is subject to increase. This is due to the delay by a number of countries in general, and Brazil in particular, in taking preventive and proactive measures to limit the spread of the COVID-19 pandemic. So, we propose to study an optimal control approach with delay in state and control variables in our mathematical model proposed by kouidere et al. which describes the dynamics of the transmission of the COVID-19. That the time with delay represent the delay to applying preventive precautions measures. Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.

Suggested Citation

  • Kouidere, Abdelfatah & Kada, Driss & Balatif, Omar & Rachik, Mostafa & Naim, Mouhcine, 2021. "Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case stu," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308304
    DOI: 10.1016/j.chaos.2020.110438
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    References listed on IDEAS

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    1. Abdelfatah Kouidere & Omar Balatif & Hanane Ferjouchia & Abdesslam Boutayeb & Mostafa Rachik, 2019. "Optimal Control Strategy for a Discrete Time to the Dynamics of a Population of Diabetics with Highlighting the Impact of Living Environment," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-8, December.
    2. Omar Balatif & Bouchaib Khajji & Mostafa Rachik, 2020. "Mathematical Modeling, Analysis, and Optimal Control of Abstinence Behavior of Registration on the Electoral Lists," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, January.
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    Cited by:

    1. 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).
    2. 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.
    3. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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