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

Ihtisham Ul Haq; Nigar Ali; Kottakkaran Sooppy Nisar

doi:10.53391/mmnsa.2022.009

Authors

Ihtisham Ul Haq Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000, Khyber Pakhtunkhwa, Pakistan https://orcid.org/0000-0002-4076-9063
Nigar Ali Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000, Khyber Pakhtunkhwa, Pakistan https://orcid.org/0000-0002-6920-3194
Kottakkaran Sooppy Nisar Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Saudi Arabia https://orcid.org/0000-0001-5769-4320

DOI:

https://doi.org/10.53391/mmnsa.2022.009

Keywords:

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

Abstract

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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