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

Abstract

In this manuscript, a qualitative analysis of the mathematical model of novel coronavirus ( -19) involving anew devised fractal-fractional operator in the Caputo sense having the fractional-order and the fractal dimension is considered. The concerned model is composed of eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery and fatality. 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 method is applied to simulate the results. At last, the results are tested with real data from -19 outbreak in Wuhan City, Hubei Province of China from 4 January to 9 March 2020, taken from a source [42] . The Numerical results are presented in terms of graphs for different fractional-order and fractal dimensions to describe the transmission dynamics of disease infection.

Mathematical modeling of COVID-19 transmission dynamics between healthcare workers and community

“…The proposed model of this paper can be further improved by considering a Fractional-order analog as well as a stochastic model in order to capture more transmission dynamics of COVID-19 [7] , [23] .…”

“…Some mathematical models were constructed to analyze the spreads of viruses [18] . During the outbreak of COVID-19, modeling attracted a special attention to many pharmacists, mathematician, chemists, biologists, epidemiologists [1] , [2] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . This can be an effective approach to study, simulate and predict the mechanism and transmission of the disease.…”

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“…In [21] , Atangana presented the fractal-fractional operators and showed the relation between Fractional and fractal calculus. For applications of fractal-fractional operators, see [22] , [23] , [24] , [25] . Because of this, modern calculus has gained more attraction as compared to classical calculus.…”

A multi-stage SEIR model to predict the potential of a new COVID-19 wave in KSA after lifting all travel restrictions

“…Based on WHO statistics, since its detection until December 25, 2020, the total number of confirmed cases worldwide is 80,133,093 and the number of deaths is 1,755,653. The considerable and continuous rise in the daily infected cases number all over the world is worrying, and many researchers are currently developing various mathematical and machine learning models to predict the future progress of this pandemic [1] , [2] , [3] , [4] , [5] , [6] , [7] . However, only few studies have discussed the possibility of the second surge of this SARS pandemic.…”