Novel Covid-19 has had a huge impact on the world's population since December 2019. The very rapid spreading of the virus worldwide, with its heavy toll of death and overload of the healthcare systems, induced the scientific community to focus on understanding, monitoring and foreseeing the epidemic evolution, weighing up the impact of different containment measures. An immense literature was produced in few months. Many papers were focused on predicting the peak features through a variety of different models. In the present paper, combining the surveillance data-set with data on mobility and testing, we develop a deterministic compartment model aimed at performing a retrospective analysis to understand the main modifications occurred to the characteristic parameters that regulate the epidemic spreading. We find that, besides self-protective behaviors, a reduction of susceptibility should have occurred in order to explain the fast descent of the epidemic after the peak. A sensitivity analysis of the basic reproduction number, in response to variations of the epidemiological parameters that can be influenced by policy-makers, shows the primary importance of a rigid isolation procedure for the diagnosed cases, combined with an intensive effort in performing extended testing campaigns. Future scenarios depend on the ability to protect the population from the injection of new cases from abroad, and to pursue in applying rigid self-protective measures.