The article develops a mathematical model for constructing a digital twin of the epidemic development process in one of the regions of the Russian Federation. We state the problem, select the model variables and perturbations, and develop a system of nonlinear differential equations to predict the output of the epidemic's relevant characteristics beyond their expected values for a given time interval. The results obtained can be used in smart city management systems, in managing the process of eliminating the consequences of the epidemic in the country's regions, as well as in simulator and training systems.