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

Abstract

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 Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in the Caputo sense (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.

Keywords

• vaccine efficacy
• non-singular kernel fractional derivative
• basic reproduction number
• stability analysis
• banach fixed-point theorem