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

A Modified SIR Model for the COVID-19 Contagion in Italy