After the outbreak of the new COVID-19 disease, the mitigation stage has been reached in most of the countries in the world . During this stage, a more accurate data analysis of the daily reported cases and other parameters became possible for the European countries and has been performed in this work . Based on a proposed parametrization model appropriate for implementation to an epidemic in a large population, we focused on the disease spread and we studied the obtained curves, as well as, investigating probable correlations between the country's characteristics and the parameters of the parametrization . We have also developed a methodology for coupling our model to the SIR-based models determining the basic and the effective reproductive number referring to the parameter space . The obtained results and conclusions could be useful in the case of a recurrence of this insidious disease in the future.