Abstract
Coronavirus disease 2019 (COVID-19), an infection that is highly contagious. It has a regrettable effect on the world and has resulted in more than 4.6 million deaths to date (July 2021). For this contagious disease, numerous nations implemented control measures. Every country has vaccination programs in place to achieve the best results. This research is done in two stages, including partial and complete vaccination, to enhance the efficiency and effectiveness of the vaccination. Our study found that receiving this vaccination lowers the risk of contracting a disease and its side effects, such as severity, hospitalization, need for oxygen, admission to the intensive care unit, and infection-related death. Taking into account, the system is built using fractional-order Caputo sense nonlinear differential equations. A basic reproduction number is calculated to determine the transmission rate. The bifurcation analysis predicts chaotic behavior of a system for this threshold value. The suggested system's recovery rate is optimized using fractional optimum controls. For the fractional-order differential equation, numerical results are simulated using MATLAB software using real-validated data (July 2021).