On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative

Highlights

• We investigate the Coronavirus (COVID-19) mathematical model spread in Wuhan Hubei Province of China recently by a novel fractional nonlocal operator (ABC).

• We study two aspects of the Model that: Qualitative aspect and Numerical aspect.

• Existence and Ulam-Hyers stability results of the model are first study by fixed point theory.

• Numerical aspect is then study by a novel method (fractional Adams Bashforth method).

• Graphical results are displayed to understand the method.

Abstract

The major purpose of the presented study is to analyze and find the solution for the model of nonlinear fractional differential equations (FDEs) describing the deadly and most parlous virus so-called coronavirus (COVID-19). The mathematical model depending of fourteen nonlinear FDEs is presented and the corresponding numerical results are studied by applying the fractional Adams Bashforth (AB) method. Moreover, a recently introduced fractional nonlocal operator known as Atangana-Baleanu (AB) is applied in order to realize more effectively. For the current results, the fixed point theorems of Krasnoselskii and Banach are hired to present the existence, uniqueness as well as stability of the model. For numerical simulations, the behavior of the approximate solution is presented in terms of graphs through various fractional orders. Finally, a brief discussion on conclusion about the simulation is given to describe how the transmission dynamics of infection take place in society.