Siberian Federal University

The article presents the compartmental differential formulation of SIR-type for modeling the dynamics of the incidence of viral infections, in particular COVID-19, taking into account the ongoing vaccination campaign and the possibility of losing immunity during some time period after vaccination or a disease. The proposed model is extended by considering the coefficients of the model as dependent on the social loyalty of the population to isolation and vaccination. This allows us to formulate the optimal control problem and build various scenarios for the development of the epidemiological situation. The results obtained on the basis of the considered models were compared with real statistical data on the incidence in the Krasnoyarsk Territory