  The purpose of this work is to give a contribution to the understanding of
the COVID-19 contagion in Italy. To this end, we developed a modified
Susceptible-Infected-Recovered (SIR) model for the contagion, and we used
official data of the pandemic up to March 30th, 2020 for identifying the
parameters of this model. The non standard part of our approach resides in the
fact that we considered as model parameters also the initial number of
susceptible individuals, as well as the proportionality factor relating the
detected number of positives with the actual (and unknown) number of infected
individuals. Identifying the contagion, recovery and death rates as well as the
mentioned parameters amounts to a non-convex identification problem that we
solved by means of a two-dimensional grid search in the outer loop, with a
standard weighted least-squares optimization problem as the inner step.
