The first diffusion of the Covid-19 outbreak in Northern Italy: an analysis based on a simplified version of the SIR model

Abstract In this paper an analysis of the first diffusion of the Covid-19 outbreak occurred in late February 2020 in Northern Italy is presented. In order to study the time evolution of the epidemic it was decided to analyze in particular as the most relevant variable the number of hospitalized people, considered as the less biased proxy of the real number of infected people. An approximate solution of the infected equation was found from a simplified version of the SIR model. This solution was used as a tool for the calculation of the basic reproduction number R 0 in the early phase of the epidemic for the most affected Northern Italian regions (Piedmont, Lombardy, Veneto and Emilia), giving values of R 0 ranging from 2.2 to 3.1. Finally, a theoretical formulation of the infection rate is proposed, introducing a new parameter, the infection length, characteristic of the disease.