The article is presented a modified simulation SEIR-model of the epidemic spread. The proposed model is created in the AnyLogic System. This model allows to estimate the restricting measures are aimed at reducing the growth of the epidemic. The calculation results are presented in four main scenarios: 1) Without restrictive measures; 2) With lite restrictive measures; 3) In the conditions of hard restrictive measures with recommended character; 4) The conditions of full quarantine and the announcement of an emergency situation. The results allow us to predict the approximate dates of the epidemic peak, the end of the epidemic, the number of deaths and the load on the health system in each of the scenarios for two cities (Moscow and St. Petersburg).