Mathematical Analysis of COVID-19 Fractional Model Incorporating Vaccination, Quarantine and Isolation Measures

Abstract

This study investigates the role of vaccination, quarantine, and isolation in controlling the spread of COVID-19 using a fractional-order mathematical model. The model consists of six non-linear fractional-order differential equations in the Caputo sense. Stability analysis is conducted using the Ulam-Hyers and modified Ulam-Hyers criteria, and the existence and uniqueness of solutions are explored with the Schauder and Banach fixed-point theorems. The model’s dynamical behavior is analyzed using the fractional Euler method. Dimensional consistency is maintained during the fractionalization process, distinguishing this study from many contemporary investigations. The results show that increasing vaccination rates, improving quarantine protocols, and enhancing isolation facilities are effective strategies for reducing COVID-19 transmission.