Values of parameters.

In this research, the ongoing COVID-19 disease by considering the vaccination strategies into mathematical models is discussed. A modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including susceptible (Sα), exposed (Eα), infected (Uα), quarantined (Qα), vaccinated (Vα), and recovered (Rα) individuals. Using conformable derivatives, a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. The basic reproduction number (R0), which is an essential indicator of disease transmission, is the subject of investigation calculating using the next-generation matrix approach. We also compute the R0 sensitivity indices, which offer important information about the relative influence of various factors on the overall dynamics. Local stability and global stability of R0 have been proved at a disease-free equilibrium point. By designing the finite difference approach of the conformable fractional derivative using the Taylor series. The present methodology provides us highly accurate convergence of the obtained solution. Present research fills research addresses the understanding gap between conceptual frameworks and real-world implementations, demonstrating the vaccination therapy’s significant possibilities in the struggle against the COVID-19 pandemic.