The consideration of infectious diseases from a mathematical point of view can reveal
possible options for epidemic control and fighting the spread of infection. However, predicting and
modeling the spread of a new, previously unexplored virus is still difficult. The present paper examines the possibility of using a new approach to predicting the statistical indicators of the epidemic
of a new type of virus based on the example of COVID-19. The important result of the study is the
description of the principle of dynamic balance of epidemiological processes, which has not been
previously used by other researchers for epidemic modeling. The new approach is also based on
solving the problem of predicting the future dynamics of precisely random values of model parameters, which is used for defining the future values of the total number of: cases (C); recovered and
dead (R); and active cases (I). Intelligent heuristic algorithms are proposed for calculating the future
trajectories of stochastic parameters, which are called the percentage increase in the total number of
confirmed cases of the disease and the dynamic characteristics of epidemiological processes. Examples are given of the application of the proposed approach for making forecasts of the considered
indicators of the COVID-19 epidemic, in Russia and European countries, during the first wave of
the epidemic.