Modeling the dynamics of COVID-19 using fractal-fractional operator with a case study

Jian-Cun Zhou; Soheil Salahshour; Ali Ahmadian; Norazak Senu

doi:10.1016/j.rinp.2021.105103

Modeling the dynamics of COVID-19 using fractal-fractional operator with a case study

Results Phys. 2022 Feb:33:105103. doi: 10.1016/j.rinp.2021.105103. Epub 2021 Dec 30.

Authors

Jian-Cun Zhou^{1

2}, Soheil Salahshour³, Ali Ahmadian^{4

5}, Norazak Senu⁶

Affiliations

¹ College of Information and Electronic Engineering, Hunan City University, Yiyang 413000, PR China.
² School of Computer Science and Engineering, Central South University, Changsha 410083, PR China.
³ Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey.
⁴ Department of Law, Economics and Human Sciences, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy.
⁵ Department of Mathematics, Near East University, Nicosia, TRNC 10, Turkey, Mersin, Turkey.
⁶ Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia.

Abstract

This research study consists of a newly proposed Atangana-Baleanu derivative for transmission dynamics of the coronavirus (COVID-19) epidemic. Taking the advantage of non-local Atangana-Baleanu fractional-derivative approach, the dynamics of the well-known COVID-19 have been examined and analyzed with the induction of various infection phases and multiple routes of transmissions. For this purpose, an attempt is made to present a novel approach that initially formulates the proposed model using classical integer-order differential equations, followed by application of the fractal fractional derivative for obtaining the fractional COVID-19 model having arbitrary order $Ψ$ and the fractal dimension $Ξ$ . With this motive, some basic properties of the model that include equilibria and reproduction number are presented as well. Then, the stability of the equilibrium points is examined. Furthermore, a novel numerical method is introduced based on Adams-Bashforth fractal-fractional approach for the derivation of an iterative scheme of the fractal-fractional ABC model. This in turns, has helped us to obtained detailed graphical representation for several values of fractional and fractal orders $Ψ$ and $Ξ$ , respectively. In the end, graphical results and numerical simulation are presented for comprehending the impacts of the different model parameters and fractional order on the disease dynamics and the control. The outcomes of this research would provide strong theoretical insights for understanding mechanism of the infectious diseases and help the worldwide practitioners in adopting controlling strategies.

Keywords: Adams–Bashforth method; COVID-19 transmission; Case study; Deterministic stability analysis; Fractal fractional order model; Newton polynomial.