  This work will study an optimal control problem describing the two-strain
SEIR epidemic model. The studied model is in the form of six nonlinear
differential equations illustrating the dynamics of the susceptibles and the
exposed, the infected, and the recovered individuals. The exposed and the
infected compartments are each divided into two sub-classes representing the
first and the second strain. The model includes two saturated rates and two
treatments for each strain. We begin our study by showing the well-posedness of
our problem. The basic reproduction number is calculated and depends mainly on
the reproduction numbers of the first and second strains. The global stability
of the disease-free equilibrium is fulfilled. The optimal control study is
achieved by using the Pontryagin minimum principle. Numerical simulations have
shown the importance of therapy in minimizing the infection's effect. By
administrating suitable therapies, the disease's severity decreases
considerably. The estimation of parameters as well as a comparison study with
COVID-19 clinical data are fulfilled. It was shown that the mathematical model
results fits well the clinical data.
