Impact of Vaccination on COVID-19 Using Fractional Operators with Non-Local Kernel
Keywords:
Atangana-Baleanu Fractional Derivative, Basic Reproduction Number, Laplace Transform, COVID-19.Abstract
This work analyzes a COVID-19 model that uses a seven-dimensional set of ordinary differential equations to account for the population’s first and second vaccination doses. We develop a mathematically nonlinear model of COVID-19 dynamics in integer order and modify it by incorporating the Atangana-Baleanu fractional derivative operator. The existence and stability conditions for the model are verified using Banach’s fixed-point theory and Picard’s successive approximation techniques. We explore how the model’s parameters affect the reproduction number. The applicability of the proposed fractional mathematical model is demonstrated through numerical simulations using memory index values of 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, and 1. Maintaining a virus-free population requires reducing transmission rates and increasing recovery rates among unvaccinated individuals. This can be achieved by rigorously adhering to preventive measures and ensuring early, adequate treatment for infected, unvaccinated individuals
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