A novel mathematical approach of COVID-19 with non-singular fractional derivative. (October 2020)

• Record Type: Journal Article
• Authors: Kumar, Sachin; Cao, Jinde; Abdel-Aty, Mahmoud
• Is Part Of: Chaos, solitons and fractals. Volume 139(2020)
• Publication Date: 2020-10
• Subjects: Fractional mathematical model -- Fractional derivative with Mittag-Leffler kernel -- COVID-19 virus -- Spectral method; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110048
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The study of COVID-19 mathematical model. Use of non-singular Mittag-Leffler kernel fractional derivative. Derivation of operational matrix of fractional differentiation for above fractional derivative. Numerical solution of a system of fractional ODE with non-singular kernel with this newly developed operational matrix. Effect of contact rate and transmissibility multiple on infected people and dynamics of all unknowns for different fractional order. Abstract: We analyze a proposition which considers new mathematical model of COVID-19 based on fractional ordinary differential equation. A non-singular fractional derivative with Mittag-Leffler kernel has been used and the numerical approximation formula of fractional derivative of function ( t − a ) n is obtained. A new operational matrix of fractional differentiation on domain [0, a ], a ≥ 1, a ∈ N by using the extended Legendre polynomial on larger domain has been developed. It is shown that the new mathematical model of COVID-19 can be solved using Legendre collocation method. Also, the accuracy and validity of our developed operational matrix have been tested. Finally, we provide numerical evidence and theoretical arguments that our new model can estimate the output of the exposed, infected and asymptotic carrier with higher fidelity than the previous models, thereby motivating the use of the presented model as a standard tool for examining the effect of contact rate and transmissibility multiple on number of infected cases are depicted with graphs.