  Optimal control problems reflecting the finding of effective quarantine
strategies are considered for two control SEIR~type models describing the
spread of the COVID-19 virus in the human population. The properties of the
corresponding optimal controls are established analytically by applying the
Pontryagin maximum principle. The optimal solutions are obtained numerically
using BOCOP 2.0.5 software. The behavior of the appropriate optimal solutions
and their dependence on the basic reproductive ratio and length of quarantine
are discussed in detail. Necessary conclusions are made.
