Inversion of a SIR-based model: a critical analysis about the application to COVID-19 epidemic

Calibration of a SIR (Susceptibles-Infected-Recovered) model with official data at international level for the COVID-19 pandemics provides a good example of the difficulties inherent the solution of inverse problems. Inverse modeling is set up in a framework of discrete inverse problems, which explicitly considers the role and the relevance of data. Together with a physical vision of the model, this is very useful to discuss the uncertainties on the data and how they influence the reliability of calibrated model parameters and, ultimately, of model predictions.