Investigation of the dynamics of COVID-19 with a fractional mathematical model: A comparative study with actual data

Ismail Gad Ameen; Hegagi Mohamed Ali; M R Alharthi; Abdel-Haleem Abdel-Aty; Hillal M Elshehabey

doi:10.1016/j.rinp.2021.103976

Investigation of the dynamics of COVID-19 with a fractional mathematical model: A comparative study with actual data

Results Phys. 2021 Apr:23:103976. doi: 10.1016/j.rinp.2021.103976. Epub 2021 Feb 19.

Authors

Ismail Gad Ameen¹, Hegagi Mohamed Ali², M R Alharthi³, Abdel-Haleem Abdel-Aty^{4

5}, Hillal M Elshehabey^{1

6}

Affiliations

¹ Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt.
² Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt.
³ Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia.
⁴ Department of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia.
⁵ Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.
⁶ Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal.

Abstract

One of the greatest challenges facing the humankind nowadays is to confront that emerging virus, which is the Coronavirus (COVID-19), and therefore all organizations have to unite in order to tackle that the transmission risk of this virus. From this standpoint, the scientific researchers have to find good mathematical models that do describe the transmission of such virus and contribute to reducing it in one way or another, where the study of COVID-19 transmission dynamics by mathematical models is very important for analyzing and controlling this disease propagation. Thus, in the current work, we present a new fractional-order mathematical model that describes the dynamics of COVID-19. In the proposed model, the total population is divided into eight classes, in addition to three compartments used to estimate the parameters and initial values. The effective reproduction number ( $R_{0}$ ) is derived by next generation matrix (NGM) method and all possible equilibrium points and their stability are investigated in details. We used the reported data (from January 23, 2020, to November 21, 2020) from the National Health Commission (NHC) of China to estimate the parameters and initial conditions (ICs) which suggested for our model. Simulation outcomes demonstrate that the fractional order model (FOM) represents behaviors that follow the real data more accurately than the integer-order model. The current work enhances the recent reported results of Zu et al. published in THE LANCET (doi:10.2139/ssrn.3539669).

Keywords: Caputo fractional derivative; Mathematical model; Novel coronavirus; Numerical simulation; Real data; Stability.