On the analysis of the fractional model of COVID-19 under the piecewise global operators

Abstract

<abstract><p>An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.</p></abstract>

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

“…For instance, several mathematical models of COVID-19 have been carried out to understand the transmission patterns [7][8][9][10][11][12][13][14][15]. The impact of the environment on the transmission dynamics of COVID-19 patterns has been studied in the given literature [16,17].…”

“…Hence, from equation (7) it is confirmed that all the solutions of the system (5) are positively invariant and within +  . 8 Next, the boundedness of the system (5) is proven. Also, the system (5) provide us…”

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

“…The examination of the migration effect in plant-pathogen-herbivore interactions was specifically conducted through the utilization of piecewise fractional analysis [ 13 ]. Another study examined the fractional model of COVID-19 by means of piecewise global operators [ 14 ]. Furthermore, the dynamics of leptospirosis disease have been explored within the confines of piecewise classical-global and classical-fractional operators [ 15 ].…”