  The most important features to assess the severity of an epidemic are its
size and its timescale. We discuss these features in a systematic way in the
context of SIR and SIR-type models. We investigate in detail how the size and
timescale of the epidemic can be changed by acting on the parameters
characterizing the model. Using these results and having as guideline the
COVID-19 epidemic in Italy, we compare the efficiency of different containment
strategies for contrasting an epidemic diffusion such as social distancing,
lockdown, tracing, early detection and isolation.
