Predicting the development of epidemic infection caused by the COVID-19 coronavirus is a matter of the utmost urgency for health care and effective anti-epidemic measures. Given the rapidly changing initial information and the ambiguous quality of data coming from various sources, it is important to quickly optimize the existing prognostic models by using more sophisticated algorithms. The aim of the study is to test the originally developed mathematical algorithms for predicting the development of the COVID-19 epidemic process. Materials and Methods. To assess the situation in China, Italy, and the USA, we used the information from Russian- and Englishlanguage sources available in official websites. The generally accepted descriptive statistics were used; mathematical modeling was based on linear regression. Statistical data processing was performed using the IBM SPSS Statistics 24.0 and R (RStudio) 3.6.0. Results. We found significant differences not only in the incidence rate of COVID-19 in the countries in question, but also in the death rate. The risk of death associated with COVID-19 is high due to the high number of severe clinical cases of the disease reported from these countries. Two preliminary regression models were created. The first, initial model was based on the increase in new cases of infection — this factor was significantly associated with the outcome; the regression coefficient was 0.02 (95% CI 0.01–0.03). In the second, expanded model, in addition to the increase in new cases, the increase in the number of severe forms of infection was also considered; the regression coefficients were 0.017 (95% CI 0.012–0.022) and 0.01 (95% CI 0.008–0.011), respectively. Adding the second variable contributed to a more accurate description of the available data by the model. Conclusion. The developed regression models for infection control and predicting the number of lethal outcomes can be successfully used under conditions of spreading diseases from the group of “new infections” when primary data received from various sourced are changing rapidly and updates of the information are continually required. In addition, our initial model can produce a preliminary assessment of the situation, and the expanded model can increase the accuracy and improve the analytic algorithm.