This paper uses Covasim, an agent-based model (ABM) of COVID-19, to evaluate and scenarios of epidemic spread in New York State (USA), the UK, and the Novosibirsk region (Russia). Epidemiological parameters such as contagiousness (virus transmission rate), initial number of infected people, and probability of being tested depend on the region’s demographic and geographical features, the containment measures introduced; they are calibrated to data about COVID-19 spread in the region of interest. At the first stage of our study, epidemiological data (numbers of people tested, diagnoses, critical cases, hospitalizations, and deaths) for each of the mentioned regions were analyzed. The data were characterized in terms of seasonality, stationarity, and dependency spaces, and were extrapolated using machine learning techniques to specify unknown epidemiological parameters of the model. At the second stage, the Optuna optimizer based on the tree Parzen estimation method for objective function minimization was applied to determine the model’s unknown parameters. The model was validated with the historical data of 2020. The modeled results of COVID-19 spread in New York State, the UK and the Novosibirsk region have demonstrated that if the level of testing and containment measures is preserved, the number of positive cases in New York State and the Novosibirsk region will remain the same during March of 2021, while in the UK it will reduce. Due to the features of the data for the Novosibirsk region (two datasets are characterized as stationary series with probability of 1), the forecast precision is relatively high for the number of hospitalizations, but is lower for new cases of COVID-19.