Vaccinations are one of the most important steps in combat against viral diseases such as COVID-19. Determining the influence of the number of vaccinated patients on the infected population represents a complex problem. For this reason, the aim of this research is to model the influence of the total number of vaccinated or fully vaccinated patients on the number of infected and deceased patients. Five separate modeling algorithms are used: Linear Regression (LR), Logistic Regression (LogR), Least Absolute Shrinkage and Selection Operator (LASSO), Multilayer Perceptron (MLP), and Support Vector Regression (SVR). Cross-correlation analysis is performed to determine the optimal lags in data to assist in obtaining better scores. The cross-validation of models is performed, and the models are evaluated using Mean Absolute Percentage Error (MAPE). The modeling is performed for four different countries: Germany, India, the United Kingdom (UK), and the United States of America (USA). Models with an error below 1% are found for all the modeled cases, with the best models being achieved either by LR or MLP methods. The obtained results indicate that the influence of vaccination rates on the number of confirmed and deceased patients exists and can be modeled using ML methods with relatively high precision.