Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan

Kamal Shah; Muhammad Arfan; Ibrahim Mahariq; Ali Ahmadian; Soheil Salahshour; Massimiliano Ferrara

doi:10.1016/j.rinp.2020.103560

Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan

Results Phys. 2020 Dec:19:103560. doi: 10.1016/j.rinp.2020.103560. Epub 2020 Nov 12.

Authors

Kamal Shah¹, Muhammad Arfan¹, Ibrahim Mahariq^{2

3}, Ali Ahmadian⁴, Soheil Salahshour⁵, Massimiliano Ferrara⁶

Affiliations

¹ Department of Mathematics, University of Malakand, Dir(L) 18800, Pakistan.
² College of Engineering and Technology, American University of the Middle East, Kuwait.
³ Department of Electrical and Electronics Engineering, University of Turkish Aeronautical Association, Ankara, Turkey.
⁴ Institute of IR 4.0, The National University of Malaysia, 43600 UKM, Bangi, Selangor, Malaysia.
⁵ Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey.
⁶ ICRIOS-The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship, Bocconi University, Department of Management and Technology Via Sarfatti, 25 20136 Milano MI, Italy.

Abstract

This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order $SIR$ type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.

Keywords: 26A33; 34B27; 45M10; ABC fractal-fractional derivative; COVID-19; Qualitative analysis; fractal-fractional Adams-Bashforth method..