Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan

• Published in: Alexandria engineering journal 2021-02, Vol.60 (1), p.477-489
• Main Authors: Ali, Zeeshan, Rabiei, Faranak, Shah, Kamal, Khodadadi, Touraj
• Format: Article
• Language: English
• Subjects: 26A33; 34A08; 93A30; Coronavirus disease model; Fractal-fractional derivative; Fractional Adams-Bashforth ([formula omitted]) method; Numerical Simulations; Stability results
• ISSN: 1110-0168; 1110-0168
• DOI: 10.1016/j.aej.2020.09.020

In this manuscript, a qualitative analysis of the mathematical model of novel coronavirus (COVID-19) involving anew devised fractal-fractional operator in the Caputo sense having the fractional-order q and the fractal dimension p is considered. The concerned model is composed of eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery and fatality. When, choosing the fractal order one we obtain fractional order, and when choosing the fractional order one a fractal system is obtained. Considering both the operators together we present a model with fractal-fractional. Under the new derivative the existence and uniqueness of the solution for considered model are proved using Schaefer’s and Banach type fixed point approaches. Additionally, with the help of nonlinear functional analysis, the condition for Ulam’s type of stability of the solution to the considered model is established. For numerical simulation of proposed model, a fractional type of two-step Lagrange polynomial known as fractional Adams-Bashforth (AB) method is applied to simulate the results. At last, the results are tested with real data from COVID-19 outbreak in Wuhan City, Hubei Province of China from 4 January to 9 March 2020, taken from a source (Ndaïrou, 2020). The Numerical results are presented in terms of graphs for different fractional-order q and fractal dimensions p to describe the transmission dynamics of disease infection.