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An epidemic disease caused by coronavirus has spread all over the world with a strong contagion rate. We present simulations of epidemic models constructed using real data to give a clear perspective and confirmation on the effect of quarantine on the evolution of the infection and the number of infected, recovered, and dead because of this epidemic in South Carolina in a time window (December 1, 2020, to June 1, 2021) when the epidemic was relatively strong. We use CDC data for infected and dead populations covering the period December 1, 2020, to June 1, 2021 in South Carolina to develop models and do simulations. There were no data available for recovered populations in this period. Part of our goal is to estimate the number of recovered for the entire period. The models and results are consistent with the data. The infection and recovery increasing in South Carolina do not show improvement in this period. The number of dead people in this period tended to increase although by small amount. Optimal control methodologies are considered where transmission, recovery, relapse of immunity and death rates are considered as decision variables in minimizing the difference between the real and computed COVID-19 infection and dead data. Effect of quarantine as intervention strategy is also considered as it is critical issue. What we want to show is what could have been the outcome if quarantine had been implemented from the very beginning. The progress of an infection in general is related not only to the present states, but also to its historical states. To account for the effect of past evolution we add fractional differential equations models.