The primary goal of this paper is to develop an approach for predicting important clinical indicators, which can be used to improve treatment. Using mathematical predictive modeling algorithms, we examined the course of COVID-19-based pneumonia (CP) with inpatient treatment. Algorithms used include dynamic and ordinary Bayesian networks (OBN and DBN), popular ML algorithms, the state-of-the-art auto ML approach and our new hybrid method based on DBN and auto ML approaches. Predictive targets include treatment outcomes, length of stay, dynamics of disease severity indicators, and facts of prescribed drugs for different time intervals of observation. Models are validated using expert knowledge, current clinical recommendations, preceding research and classic predictive metrics. The characteristics of the best models are as follows: MAE of 3.6 days of predicting LOS (DBN plus FEDOT auto ML framework), 0.87 accuracy of predicting treatment outcome (OBN); 0.98 F1 score for predicting facts of prescribed drug (DBN). Moreover, the advantage of the proposed approach is Bayesian network-based interpretability, which is very important in the medical field. After the validation of other CP datasets for other hospitals, the proposed models can be used as part of the decision support systems for improving COVID-19-based pneumonia treatment. Another important finding is the significant differences between COVID-19 and non-COVID-19 pneumonia.