The observed spread of coronavirus infection across Russian regions, as a first approximation, obeys the classic laws of diffusion of innovations. The article describes in detail theoretical approaches to the analysis of the spread of social diseases and discusses methodological limitations that reduce the possibility of predicting such phenomena and affect decision-making by the authorities. At the same time, we believe that for most regions, including Moscow, until May 12, 2020, the dynamics of confirmed cases are a reduced and delayed reflection of actual processes. Thus, the introduced self-isolation regime in Moscow and other agglomerations affected the decrease in the number of newly confirmed cases two weeks after its introduction. In accordance with our model, at the first stage, carriers infected abroad were concentrated in regions with large agglomerations and in coastal and border areas with a high intensity of internal and external links. Unfortunately, the infection could not be contained, and it started growing exponentially across the country. By mid-April 2020, cases of the disease were observed in all Russian regions; however, the remotest regions least connected with other parts of Russia and other countries had only isolated cases. By mid-May, at least in Moscow, the number of new cases began to decline, which created the prerequisites for reducing restrictions on the movement of residents. However, the decrease in the number of new cases after passing the peak of the epidemic in May is slower than the increase at the beginning. These facts contradict the diffusion model; thus, the model is not applicable for epidemiological forecasts based on empirical data. Using econometric methods, it is shown that for different periods of diffusion, various characteristics of the regions affect the spread of the disease. Among these features we note the high population density in cities, proximity to the largest metropolitan areas, higher proportion of the most active and frequently traveling part of the population (innovators, migrants), and intensive ties within the community, as well as with other regions and countries. The virus has spread faster in regions where the population has a higher susceptibility to diseases, which confirms the importance of the region's health capital. The initial stage was dominated by random factors. We conclude this paper with directions for further research.