Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease
that has afiected millions of people worldwide. Initially, basic public health measures
were implemented to control specially the spread of such virus. However, vaccination has
emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent
spread of the disease. In this study, a modeling approach is used to analyze the impact
of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical
method, the model is solved based on reported cases in Pakistan. A spectral method is
employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known
as R0, which indicates the potential for disease transmission. The study also includes
a detailed stability analysis, examining the invariance properties of the model solution
and discussing equilibrium points and their stability in disease-free and endemic states.
Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.