Since the outbreak of coronavirus disease-2019 (COVID-19), the whole world has taken interest in the mechanisms of its spread and development. Mathematical models have been valuable instruments for the study of the spread and control of infectious diseases. For that purpose, we propose a two-way approach in modeling COVID-19 spread: a susceptible, exposed, infected, recovered, deceased (SEIRD) model based on differential equations and a long short-term memory (LSTM) deep learning model. The SEIRD model is a compartmental epidemiological model with included components: susceptible, exposed, infected, recovered, deceased. In the case of the SEIRD model, official statistical data available online for countries of Belgium, Netherlands, and Luxembourg (Benelux) in the period of March 15 2020 to March 15 2021 were used. Based on them, we have calculated key parameters and forward them to the epidemiological model, which will predict the number of infected, deceased, and recovered people. Results show that the SEIRD model is able to accurately predict several peaks for all the three countries of interest, with very small root mean square error (RMSE), except for the mild cases (maximum RMSE was 240.79 ± 90.556), which can be explained by the fact that no official data were available for mild cases, but this number was derived from other statistics. On the other hand, LSTM represents a special kind of recurrent neural network structure that can comparatively learn long-term temporal dependencies. Results show that LSTM is capable of predicting several peaks based on the position of previous peaks with low values of RMSE. Higher values of RMSE are observed in the number of infected cases in Belgium (RMSE was 535.93) and Netherlands (RMSE was 434.28), and are expected because of thousands of people getting infected per day in those countries. In future studies, we will extend the models to include mobility information, variants of concern, as well as a medical intervention, etc. A prognostic model could help us predict epidemic peaks. In that way, we could react in a timely manner by introducing new or tightening existing measures before the health system is overloaded.