A simple but complex enough -SIR type model to be used with COVID-19 real data. Application to the case of Italy

Since the start of the COVID-19 pandemic in China many models have appeared in the literature, trying to simulate its dynamics. Focusing on modeling the biological and sociological mechanisms which influence the disease spread, the basic reference example is the SIR model. However, it is too simple to be able to model those mechanisms (including the three main types of control measures: social distancing, contact tracing and health system measures) to fit real data and to simulate possible future scenarios. A question, then, arises: how much and how do we need to complexify a SIR model? We develop a $$ -SEIHQRD model, which may be the simplest one satisfying the mentioned requirements for arbitrary territories and can be simplified in particular cases. We show its very good performance in the Italian case and study different future scenarios.