Describing the COVID-19 outbreak during the lockdown: fitting modified SIR models to data

In this paper, we analyse the COVID-19 outbreak data with simple modifications of the SIR compartmental model, in order to understand the time evolution of the cases in Italy and Germany, during the first half of 2020. Even if the complexity of the pandemic cannot be easily described, we show that our models are suitable for understanding the data during the application of the social distancing and the lockdown. We compare and contrast different modifications of the SIR model showing the strengths and the weaknesses of each approach. Finally, we discuss the reliability of the model predictions for estimating the near- and far-future evolution of the outbreak.