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The worldwide spread of a new infection SARS-CoV-2 makes relevant the analysis of the different factors that lead to the vulnerability of modern civilization to previously unknown diseases. In this regard, the development of mathematical models describing the evolution of epidemics like COVID-19 and the identification of socio-economic factors affecting the epidemiological situation in regions is an important research task. The paper proposes a probabilistic mathematical model for the spread of the COVID-19 epidemic, which allows to analyze the evolution of the main characteristics of the disease and to assess main factors influencing them. The study is based on the official statistical data on the spread of the COVID 19 presented on coronavirus sites in the Russian Federation and other countries, the Yandex Data Lens dataset service, as well as the data from the Federal State Statistics Service. In the research some data mining methods were used for evaluation the model’s parameters. The model equations allow to predict the evolution of the disease and estimate the confidence interval of such prognosis. We estimated the ratio of detected and hidden cases of the disease, the distribution of the disease’s duration probability and its average value for different regions. It has been mathematically proven that the vaccination is the necessary and sufficient condition of achievement a stationary stable state - the cessation of a pandemic. The regions of Russian Federation were clustered by the course of the disease COVID-19 on the base of k-means method. The analysis of the most important socio-economic factors affecting the epidemiological situation was provided separately for each cluster.

Model of socio-economic factors in the spread of SARS-CoV-2 across Russian regions