The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization technique. In this way, we are able to evaluate for each of the three above-mentioned scenarios the daily number of infectious cases from today until the end of virus spreading, the day(s) in which this number will be at its highest peak, and the day in which the infected cases will become very close to zero.