In recent years, there has been an increased focus among researchers finding the best and most efficient method for managing infectious diseases. The concept of optimal control has been used extensively in recent times to address the COVID-19 pandemic’s spread. To demonstrate the virus’s constant rates of transmission, we examine a mathematical model in this article. On the model with two distinct situations, an optimum control strategy is implemented. Treatment and immunization rates are two controls in the first scenario. This work uses mathematical modeling, an optimum control approach applying the Hamilton method, and Pontryagin’s maximum principle to determine the effects of various control methods as time-dependent interventions. According to computational studies, high-level therapy has the largest influence on minimizing the total number of people that are infected. Additionally, using the forward–backward Runge–Kutta technique in MATLAB, the mathematical with and without control variables solved for initial states and parameters. The results of this optimal control study imply that the recommended scenarios might be applied methods for reducing the population’s infection rate and improve public health strategies successfully.