COVID-19 pandemic course 2020-2022: description by methods of mathematical statistics and discrete mathematical analysis

The paper describes the course of the COVID-19 pandemic using a combination of mathematical statistics and discrete mathematical analysis (DMA) methods. The method of regression derivatives and FCARS algorithm as components of DMA will be for the first time tested outside of geophysics problems. The algorithm is applied to time series of the number of new cases of COVID-19 infections per day for some regions of Russia and the Republic of Austria. This allowed to assess the nature and anomalies of pandemic spread as well as restrictive measures and decisions taken in terms of the administration of countries and territories. It was shown that these methods can be used to identify time intervals of change in the nature of the incidence rate and areas with the most severe course of the epidemic. This made it possible to identify the most significant restrictive measures that allowed to reduce the growth of the disease.