Corona vaccination is the most effective technique for controlling the covid -19 pandemic. Given the size of a nation like India, a shortage of vaccine was also a significant issue in the early days. The current work used an optimization technique to develop a mathematical model for vaccination of various age groups. Mortality, symptomatic infection, non -ICU patient, and hospitalized patient are the four distinct models. In the case of vaccination, one might assert that it is 50% effective and has been shown to be a successful method of averting corona epidemics. The primary issue in the early days was how to run a successful immunization program. Allocating vaccines to various age groups proved to be another challenge. Vaccines were first distributed in India according to age categories. Following this, a large immunization effort was carried out. In the current work, this vaccine approach was investigated mathematically as a model.