Describing the COVID-19 Outbreak Fitting Modified SIR models to Data

In this paper we fit simple modifications of the SIR compartmental model to the COVID-19 outbreak data, available from official sources for Italy and other countries. Even if the complexity of the pandemic can not be easily modelled, we show that our model, at present, describes the time evolution of the data in spite of the application of the social distancing and lock-down procedure. Finally, we discuss the reliability of the model predictions, under certain conditions, for estimating the near and far future evolution of the COVID-19 outbreak. The conditions for the applicability of the proposed models are discussed.