Open Access

ARTICLE

Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

Zafar Iqbal^1,2, Muhammad Aziz-ur Rehman¹, Nauman Ahmed^1,2, Ali Raza^3,4, Muhammad Rafiq⁵, Ilyas Khan^6,*, Kottakkaran Sooppy Nisar⁷
1 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
3 Stochastic Analysis & Optimization Research Group, Department of Mathematics, Air University, Islamabad, 44000, Pakistan
4 Department of Mathematics, National College of Business Administration and Economics, Lahore, Pakistan
5 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, 54500, Pakistan
6 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915, Vietnam
7 Department of Mathematics, College of Arts and Science at Wadi Aldawaser, Prince Sattam Bin Abdulaziz University, Alkharj, 11991, Kingdom of Saudi Arabia
* Corresponding Author: Ilyas Khan. Email:
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)

Computers, Materials & Continua 2022, 71(2), 2141-2157. https://doi.org/10.32604/cmc.2022.013906

Received 30 August 2021; Accepted 10 November 2021; Issue published 07 December 2021

Abstract

In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented.

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Keywords

Coronavirus pandemic model; deterministic ordinary differential equations; numerical methods; convergence analysis

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