Modeling and Analysis of Novel Covid-19 Under Fractal-Fractional Derivative With Case Study of Malaysia

Abstract

In this paper, new model on novel coronavirus disease ([Formula: see text]-19) with four compartments including susceptible, exposed, infected, and recovered class with fractal-fractional derivative is proposed. Here, Banach and Leray–Schauder alternative type theorems are used to establish some appropriate conditions for the existence and uniqueness of the solution. Also, stability is needed in respect of the numerical solution. Therefore, Ulam–Hyers stability using nonlinear functional analysis is used for the proposed model. Moreover, the numerical simulation using the technique of fundamental theorem of fractional calculus and the two-step Lagrange polynomial known as fractional Adams-Bashforth [Formula: see text] method is proposed. The obtained results are tested on real data of [Formula: see text]-19 outbreak in Malaysia from 25 January till 10 May 2020. The numerical simulation of the proposed model has performed in terms of graphs for different fractional-order [Formula: see text] and fractal dimensions [Formula: see text] via number of considered days of disease spread in Malaysia. Since [Formula: see text]-19 transmits rapidly, perhaps, the clear understanding of transmission dynamics of [Formula: see text]-19 is important for countries to implement suitable strategies and restrictions such as Movement Control Order (MCO) by the Malaysian government, against the disease spread. The simulated results of the presented model demonstrate that movement control order has a great impact on the transmission dynamics of disease outbreak in Malaysia. It can be concluded that by adopting precautionary measures as restrictions on individual movement the transmission of the disease in society is reduced. In addition, for such type of dynamical study, fractal-fractional calculus tools may be used as powerful tools to understand and predict the global dynamics of the mentioned disease in other countries as well.

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach

“…Recently, the dynamics of COVID-19 pandemic have been addressed with the help of ABC fractional operator in [22] . The application of various fractal-fractional operators in epidemiology can be found in [23] , [24] .…”

Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittage-Leffler kernel

“…The concept between fractional and fractal calculus is first presented by Atangana [21] , [22] . Since then, many applications both conditional and numerical study of fractional-order differential and integral equations for application of the fractal-fractional derivative has been extensively studied [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] . The fractal-fractional DEs change the order and as well as dimension of the equation to rational form.…”

Investigation of fractal-fractional order model of COVID-19 in Pakistan under Atangana-Baleanu Caputo (ABC) derivative

“…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.…”