The use of artificial neural networks (ANNs) is a great contribution to medical studies since the application of forecasting concepts allows for the analysis of future diseases propagation. In this context, this paper presents a study of the new coronavirus SARS-COV-2 with a focus on verifying the virus propagation associated with mitigation procedures and massive vaccination campaigns. There were two proposed methodologies in making predictions 28 days ahead for the number of new cases, deaths, and ICU patients of five European countries: Portugal, France, Italy, the United Kingdom, and Germany. A case study of the results of massive immunization in Israel was also considered. The data input of cases, deaths, and daily ICU patients was normalized to reduce discrepant numbers due to the countries' size and the cumulative vaccination values by the percentage of population immunized (with at least one dose of the vaccine). As a comparative criterion, the calculation of the mean absolute error (MAE) of all predictions presents the best methodology, targeting other possibilities of use for the method proposed. The best architecture achieved a general MAE for the 1-to-28-day ahead forecast, which is lower than 30 cases, 0.6 deaths, and 2.5 ICU patients per million people.