A vigorous study of fractional order COVID-19 model via ABC derivatives

Abstract

The newly arose irresistible sickness known as the Covid illness (COVID-19), is a highly infectious viral disease. This disease caused millions of tainted cases internationally and still represent a disturbing circumstance for the human lives. As of late, numerous mathematical compartmental models have been considered to even more likely comprehend the Covid illness. The greater part of these models depends on integer-order derivatives which cannot catch the fading memory and crossover behavior found in many biological phenomena. Along these lines, the Covid illness in this paper is studied by investigating the elements of COVID-19 contamination utilizing the non-integer Atangana-Baleanu-Caputo derivative. Using the fixed-point approach, the existence and uniqueness of the integral of the fractional model for COVID is further deliberated. Along with Ulam-Hyers stability analysis, for the given model, all basic properties are studied. Furthermore, numerical simulations are performed using Newton polynomial and Adams Bashforth approaches for determining the impact of parameters change on the dynamical behaviour of the systems.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

“…Thus, using a fractional derivative to build up a COVID-19 model may address gaps between data and the existing knowledge on the COVID-19 transmission process. However, in all of the existing fractional order models on COVID-19 [25] , [26] , [27] , [28] , [82] , [83] , [84] , [85] , instead of taking fractional derivatives in the force of infection in disease transmission, authors used fractional derivatives only in the population (left-hand side of the system replacing ordinary derivatives with some fractional order derivative), which in general a Markovian process [20] , [21] , [35] , [36] , [38] . Consequently, these models may not be appropriate to study the power law/memory effect in the transmission process of COVID-19.…”

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

“…A recent study is conducted for the understanding of coronavirus infection and its controls [27]. A mathematical model in non-singular order to investigate the coronavirus infection is considered in [28]. Nonetheless, some studies show that in some conditions, time-varying fractional-order models are able to better demonstrate behavior of systems [40][41][42][43][44][45][46][47].…”

Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection

“…Using the third layer of COVID-19 cases in Li et al (2021c) , the authors formulated a mathematical model and suggested the results for infection control. A study on the coronavirus infection fractional order is suggested in Li et al (2021d) . The infection of COVID-19 in Nigeria through a mathematical model is explored in Iboi et al (2020a) .…”