Estimating Uncertainty in Epidemic Models: An Application to COVID-19 Pandemic in Italy

Traditional epidemic models, like the classical SIR, are fitted to real data using deterministic optimization techniques. As a consequence, their performances cannot be properly assessed and, more importantly, the estimates of the critical epidemic parameters (which are of dramatic importance in monitoring the epidemic evolution) cannot be complemented with the calculation of confidence intervals. The aim of the present work is to remove such limitations and to compare the results obtained using two stochastic versions of deterministic SIR models. We describe the two alternatives and the associated estimation procedures, and we apply the two methodologies to a set of COVID-19 data observed in Italy in the 2020 pandemic wave. Our estimates of the basic reproduction number are comparable with the official sources, but using our methods uncertainty can also be properly assessed.