In the structure of infectious diseases in the Yaroslavl region, more than 90 % are influenza and acute respiratory viral infections (ARVI). Influenza occupies a special place among human infectious diseases. This is due to its ability to epidemic and pandemic spread in a relatively short time. In this regard, scientific research on the analysis and forecasting of probable scenarios for the development of epidemic processes is of particular importance. The work used the data of the forms of the federal state statistical observation No. 2 “Information on infectious and parasitic diseases”. Fourier analysis was used to process time series. The significance of the mathematical model was checked using the Fisher test. The table of critical values of the Fisher criterion was used to assess the statistical significance, the significance level was taken equal to 0.05. Data processing was carried out using MS Excel 2013 software. During the study of the dynamics of the epidemic process, the trend of reducing the incidence of influenza and ARVI in the Yaroslavl region over the past 36 years has been determined. The dynamics of the incidence of influenza and ARVI in the Yaroslavl region over the past 36 years has a tendency to decrease. As a result of calculations, we obtained cyclical components with periods equal to 3 and 5 years. This is due to the accumulation of people who are not immune to these infections. Mathematical calculations have confirmed the values of seasonal fluctuations in 6 and 12 months. The maximum number of sick people is recorded in the winter-spring period (February — March). In accordance with the calculations, a decrease in the incidence of influenza and ARVI in the Yaroslavl region is expected in the period from 2020 to 2022: in 2020 the number of sick people (per 100 thousand population) is predicted to be 20 962.64, in 2021 — 18 138.58.