Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator

Rahat Zarin; Amir Khan; Aurangzeb; Ali Akgül; Esra Karatas Akgül; Usa Wannasingha Humphries; Rahat Zarin; Amir Khan; Aurangzeb; Ali Akgül; Esra Karatas Akgül; Usa Wannasingha Humphries

doi:10.3934/math.2022872

AIMS Mathematics

2022, Volume 7, Issue 9: 15939-15964. doi: 10.3934/math.2022872

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Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator

1.
Department of Basic Sciences, University of Engineering and Technology Peshawar, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
3.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
4.
Siirt University, Art and Science Faculty of Science, Department of Mathematics, TR-56100 Siirt, Turkey

Received: 27 February 2022 Revised: 18 April 2022 Accepted: 27 April 2022 Published: 28 June 2022
MSC : 37G05, 37G15, 39A28, 92B05

In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.
- real data,
- pandemic model,
- stability analysis,
- sensitivity analysis,
- numerical simulations
Citation: Rahat Zarin, Amir Khan, Aurangzeb, Ali Akgül, Esra Karatas Akgül, Usa Wannasingha Humphries. Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator[J]. AIMS Mathematics, 2022, 7(9): 15939-15964. doi: 10.3934/math.2022872

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Abstract

In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.

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