A Detailed Mathematical Analysis of the Vaccination Model for COVID-19

This study aims to structure and evaluate a new COVID-19 model which predicts vaccination effect in the Kingdom of Saudi Arabia (KSA) under Atangana-Baleanu-Caputo (ABC) fractional derivatives. On statistical aspect, we analyze collected data fully vaccinated people from June 01, 2021, February 15, 2022. Then apply Eviews program find best for predicting against this pandemic, based on daily series 16, 2022, April The results analysis show that appropriate is autoregressive integrated moving average ARIMA (1, 1, 2), hence, forecast about evolution theCOVID-19 60 days presented. theoretical aspect provides equilibrium points, reproduction number , biologically feasible region proposed model. Also, obtain existence uniqueness by using Picard-Lindel method iterative scheme with Laplace transform. numerical generalized Adams-Bashforth technique order simulate Moreover, simulations are performed dependent real KSA plots effects fractional-order operator anticipation suggested approximation will be better than established traditional Finally, concerned compared exact available date given aspect.