A stochastic model of the social distancing interventions to contain the Covid-19 pandemic: comparison with the Italian case

A SIR-derived stochastic model is developed to study the spread of a virus such as the SARS-CoV-2 in a population, where relationships among individuals can be interrupted to simulate lockdowns of different intensity. Social distancing and limited hospitals capacity can also be taken into account. The properties of the model are discussed and suggestions to limit the impact of the pandemic, the number of hospitalised people and of deaths are derived. The model is also used to analyse the first and the beginning of the second wave of the contagion in Italy.