ABSTRACT
Currently, the entire planet is suffering from a contagious epidemic infection, 2019-nCOV due to newly detected coronavirus. This is a lethal infectious virus that has destroyed thousands of lives all over the world. The important aim of this study is to investigate a susceptible-infected-treatment-recovered (SITR) model of coronavirus (2019-nCOV) with bi-modal virus spread in a susceptible population. The considered 2019-nCOV model is analyzed by two fractional derivatives: the Caputo and Atangana-Baleanu-Caputo (ABC). For the Caputo model, we present a few basic mathematical characteristics such as existence, positivity, boundedness and stability result for disease-free equilibria. The fixed-point principle is used to establish the existence and uniqueness conditions for the ABC model solution. We employed the Adams-Bashforth-Moulton (ABM) numerical technique for the Caputo model solution and the Toufik-Atangana (TA) numerical approach for the ABC model solution. Finally, using MATLAB, the simulation results are shown to highlight the impact of arbitrarily chosen fractional-order and model parameters on infection dynamics. © 2022 The Author(s).
ABSTRACT
The purpose of this research is to explore the spread dynamics of a novel coronavirus outbreak, or 2019-nCOV via a fractional approach of type fractal-fractional (FF) derivative. We considered the FF approach in sense of the Atangana-Baleanu derivative for the system 2019-nCOV. In the FF operator, when we choose fractional-order one, we achieve the fractal model and when choosing fractal order one then we obtain a fractional model and while considering both the operators together we obtain the fractal-fractional model. The obtained results show via graphics for the different collections of fractal and fractional orders. The graphical results show the new operator impacts on a practical situation in a more visual way. © 2022
ABSTRACT
Abstract Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID-19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID-19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases. The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary-order coronavirus disease system. This system illustrating the probability of spread within a given general population. In this work, we considered a system of a novel COVID-19 with the three various arbitrary-order derivative operators: Caputo derivative having the power law, Caputo?Fabrizio derivative having exponential decay law and Atangana?Baleanu-derivative with generalized Mittag?Leffler function. The existence and uniqueness of the arbitrary-order system is investigated through fixed-point theory. We investigate the numerical solutions of the non-linear arbitrary-order COVID-19 system with three various numerical techniques. For study, the impact of arbitrary-order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power ?.