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.