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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. • A systematic analysis of the epidemic spread and characteristics of the new COVID-19 disease. • Specific parameterization model which facilitates the analytical mathematical description and understanding. • Methodology of coupling this model with the SIR-based models and determine the basic reproductive number. • Analysis of the daily reported cases in the European countries. • Statistically significant correlations between the epidemic's parameters were studed. [ABSTRACT FROM AUTHOR]