  Background. The paper concerns the SARS-CoV2 (COVID-19) pandemic that,
starting from the end of February 2020, began spreading along the Italian
peninsula, by first attacking small communities in north regions, and then
extending to the center and south of Italy, including the two main islands.
  Objective. The creation of a forecast model that manages to alert the
decision-making bodies and, in particular, the healthcare system, to hinder the
emergence of any other pandemic outbreaks, or the arrival of subsequent
pandemic waves.
  Methods. A new mathematical model to describe the pandemic is given. The
model includes the class of undiagnosed infected people, and has a multi-region
extension, to cope with the in-time and in-space heterogeneity of the epidemic.
  Results. We obtain a robust and reliable tool for the forecast of the total
and active cases, which can be also used to simulate different scenarios.
  Conclusions. We are able to address a number of issues, such as assessing the
adoption of the lockdown in Italy, started from 11 March 2020, and how to
employ a rapid screening test campaign for containing the epidemic.
