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Optimal control of a fractional order model for the COVID – 19 pandemic

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  • Baba, Bashir Abdullahi
  • Bilgehan, Bulent

Abstract

In this paper a fractional optimal control problem was formulated for the outbreak of COVID-19 using a mathematical model with fractional order derivative in the Caputo sense. The state and co-state equations were given and the best strategy to significantly reduce the spread of COVID-19 infections was found by introducing two time-dependent control measures, u1(t)(which represents the awareness campaign, lockdown, and all other measures that reduce the possibility of contacting the disease in susceptible human population) and u2(t)(which represents quarantine, monitoring and treatment of infected humans). Numerical simulations were carried out using RK-4 to show the significance of the control functions. The exposed population in susceptible population is reduced by the factor (1−u1(t)) due to the awareness and all other measures taken. Likewise, the infected population is reduced by a factor of (1−u2(t)) due to the monitoring and treatment by health professionals.

Suggested Citation

  • Baba, Bashir Abdullahi & Bilgehan, Bulent, 2021. "Optimal control of a fractional order model for the COVID – 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100031x
    DOI: 10.1016/j.chaos.2021.110678
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    References listed on IDEAS

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    1. Min Zhao & Yanzhen Wang & Lansun Chen, 2012. "Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, August.
    2. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2020. "Save the pine forests of wilt disease using a fractional optimal control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Al-Mdallal, Qasem M. & Abu Omer, Ahmed S., 2018. "Fractional-order Legendre-collocation method for solving fractional initial value problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 74-84.
    4. Tatiana Odzijewicz & Agnieszka B. Malinowska & Delfim F. M. Torres, 2012. "Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, May.
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    2. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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