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ARTICLE

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator

by Olumuyiwa J. Peter¹, Amjad S. Shaikh^2,*, Mohammed O. Ibrahim¹, Kottakkaran Sooppy Nisar³, Dumitru Baleanu^4,5,6, Ilyas Khan⁷, Adesoye I. Abioye¹

1 Department of Mathematics, University of Ilorin, Ilorin, Kwara, Nigeria
2 Department of Mathematics, AKI’s Poona College of Arts, Science and Commerce, Camp, Pune, India
3 Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia
4 Department of Mathematics, Cankaya University, Ankara, 06790, Turkey
5 Institute of Space Sciences, Magurele-Bucharest, 077125, Romania
6 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan
7 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

* Corresponding Author: Amjad S. Shaikh. Email:

(This article belongs to the Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)

Computers, Materials & Continua 2021, 66(2), 1823-1848. https://doi.org/10.32604/cmc.2020.012314

Received 25 June 2020; Accepted 30 August 2020; Issue published 26 November 2020

Abstract

We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R₀ is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.

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