Open Access

ARTICLE

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

Zafar Iqbal1,2, Muhammad Aziz-ur Rehman1, Nauman Ahmed1,2, Ali Raza3,4, Muhammad Rafiq5, Ilyas Khan6,*, 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 the 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

## 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.

## Keywords

APA Style
Iqbal, Z., Rehman, M.A., Ahmed, N., Raza, A., Rafiq, M. et al. (2022). Structure preserving algorithm for fractional order mathematical model of COVID-19. Computers, Materials & Continua, 71(2), 2141-2157. https://doi.org/10.32604/cmc.2022.013906
Vancouver Style
Iqbal Z, Rehman MA, Ahmed N, Raza A, Rafiq M, Khan I, et al. Structure preserving algorithm for fractional order mathematical model of COVID-19. Comput Mater Contin. 2022;71(2):2141-2157 https://doi.org/10.32604/cmc.2022.013906
IEEE Style
Z. Iqbal et al., "Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19," Comput. Mater. Contin., vol. 71, no. 2, pp. 2141-2157. 2022. https://doi.org/10.32604/cmc.2022.013906

View

Like

## Related articles

• Xiaonan Hou, Hong Hu, Yanping...
• N.J. Bartle, P.D. Gosling
• Chein-Shan Liu
• Ming-Hsiao Lee, Wen-Hwa Chen
• D.L. Young, C.C. Tsai, Y.C. Lin,...