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Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed a MSIlIhR-V mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobian matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model's stability and instability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of COVID-19 from 4 January, 2021 up to 14 June, 2021 in Iran. Maple and MATLAB software's will be used for programming. We will use Maple software for analytical parts and MATLAB software for numerical and simulation parts. [ABSTRACT FROM AUTHOR]