Before revision:  In the second part of the note, we apply our model to the COVID-19 epidemics in Northern Italy, by numerical simulations based on estimate of certain parameters on the basisof medical evidence, and on fit of the other parameters from data on the first decade of March; the simulations reproduce quite satisfactorily the developements in the subsequent week, at difference with the standard SIR model. Our simulations show that if no actions were taken, the estimates based on this model would be about one third of those based on the SIR model as far as the height of the epidemic peak is concerned, and about half for what concerns the time scale of the epidemics.
After revision:  We discuss how a SIR-based prediction of the epidemic course based on early data but not taking into account the presence of a large set of asymptomatic infectives would give wrong estimate of very relevant quantities such as the epidemic peak is concerned, and about half for what concerns the time scale of the epidemics.