ABSTRACT
The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variables