The paper concerns a new forecast model that includes the class of undiagnosed infected people, and has a multiregion extension, to cope with the in-time and in-space heterogeneity of an epidemic. The model is applied to 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. It has proved to be a robust and reliable tool for the forecast of the total and active cases, which can be also used to simulate different scenarios. In particular, the model is able to address a number of issues, such as assessing the adoption of the in Italy, started from March 11, 2020; the estimate of the actual attack rate; and how to employ a rapid screening test campaign for containing the epidemic.
