An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model


  • Ihtisham Ul Haq Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000, Khyber Pakhtunkhwa, Pakistan
  • Nigar Ali Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000, Khyber Pakhtunkhwa, Pakistan
  • Kottakkaran Sooppy Nisar Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Saudi Arabia



Caputo fractional derivative, optimal control strategy, Grünwald-Letnikov numerical method, stability analysis


In this article, a mathematical model of the COVID-19 pandemic with control parameters is introduced. The main objective of this study is to determine the most effective model for predicting the transmission dynamic of COVID-19 using a deterministic model with control variables. For this purpose, we introduce three control variables to reduce the number of infected and asymptomatic or undiagnosed populations in the considered model. Existence and necessary optimal conditions are also established. The Grünwald-Letnikov non-standard weighted average finite difference method (GL-NWAFDM) is developed for solving the proposed optimal control system. Further, we prove the stability of the considered numerical method. Graphical representations and analysis are presented to verify the theoretical results.


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How to Cite

Haq, I. U., Ali, N., & Nisar, K. S. (2022). An optimal control strategy and Grünwald-Letnikov finite-difference numerical scheme for the fractional-order COVID-19 model. Mathematical Modelling and Numerical Simulation With Applications, 2(2), 108–116.



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