Solution of a dynamical memory effect COVID-19 infection system with leaky vaccination efficacy by non-singular kernel fractional derivatives

Abstract

<abstract><p>In this paper, the recent trends of CoVID-19 infection spread have been studied to explore the advantages of leaky vaccination dynamics in SEVR (Susceptible Effected Vaccinated Recovered) compartmental model with the help of <italic>Caputo-Fabrizio</italic> (CF) and <italic>Atangana-Baleanu derivative in the Caputo sense</italic> (ABC) non-singular kernel fractional derivative operators with memory effect within the model to show possible long–term approaches of the infection along with limited defensive vaccine efficacy that can be designed numerically over the closed interval ranging from 0 to 1. One of the main goals is to provide a stepping information about the usefulness of the aforementioned non-singular kernel fractional approaches for a lenient case as well as a critical case in CoVID-19 infection spread. Another is to investigate the effect of death rate on state variables. The estimation of death rate for state variables with suitable vaccine efficacy has a significant role in the stability of state variables in terms of basic reproduction number that is derived using next generation matrix method, and order of the fractional derivative. For non-integral orders the pandemic modeling sense viz, CF and ABC, has been compared thoroughly. Graphical presentations together with numerical results have proposed that the methodology is powerful and accurate which can provide new speculations for CoVID-19 dynamical systems.</p></abstract>

Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

“…(iii) Let us prove that F(B R ) = {F(u) : u ∈ B R } is relatively compact in E γ,p . Let t ∈ (0, 1) and h > 0, where t + h ≤ 1, and let u ∈ D R . From (12), we obtain that…”

“…It is noticeable, in recent years, that the field of fractional calculus has been swept for research by many mathematicians, due to its effectiveness in describing many physical phenomena, see, e.g., [1][2][3][4][5][6][7].…”

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

“…The Atangana-Baleanu fractional derivative have given successful representations in real world systems described by the heat fractional equation or the diffusion fractional equation, see for example [34][35][36]. The Covid-19 infection spread have been studied by introducing fractional model with the help of Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense [37], also the Atangana-Baleanu derivative has been considered for the analysis of Lévy noise driven Hepatitis B virus (HBV) infectious disease by considering the vaccination effect on its dynamical behavior [38]. Other important fields that recently have attract the attention of several researchers is the modeling of different systems by mixing different fractional derivatives, like the Caputo derivative with the Atangana-Baleanu and other fractional derivatives in the same model, see for example [39].…”

Fractional COVID-19 Modeling and Analysis on Successive Optimal Control Policies

“…The global and local dynamics of COVID-19 may be completely characterized by mathematical models operating under fractional order derivatives. In addition, models of this type that make use of fractional calculus are superior in terms of their ability to precisely and accurately represent observed occurrences [49][50][51][52][53][54][55][56][57]. The researchers utilize models to track the evolution epidemic over a period of time, such as SEIR [58], which considers four compartments: Susceptible Exposed, Infected and Recovered.…”