Non-singular kernel-based time-fractional order Covid-19 mathematical model with vaccination

Recently, numerous demonstrative investigations on the mathematical modelling and analysis of Covid-19 have been performed. In this regard, a mathematical model is introduced to demonstrate the effects of vaccination on Covid-19. This study presents the five compartmental groups of the model, namely susceptible, infected, exposed, recovered groups, and vaccinated people. To make the model more realistic, the existing integer-order system has been modified using the Mittag–Leffler kernel. The formation of a fractional-order model shows the validity of this generalization with memory. In addition to the positivity solution, existence, uniqueness, and biologically feasible region are considered. The Ulam–Hyers stability is established through fixed-point theory and nonlinear analysis. The basic reproduction number, which means the number of people predicted to be secondarily infected among the susceptible population, is calculated. The considered model is assessed by using the Atangana–Baleanu fractional operator, and the fractional Adams–Bashforth numerical technique based on Lagrange polynomial interpolation is adopted to solve the model. Further, the error analysis of the present method has also been included. The behaviour of the solution is demonstrated through numerical simulations with the help of graphical representations.