A Bayesian approach for monitoring epidemics in presence of undetected cases

One of the key indicators used in tracking the evolution of an infectious disease is the reproduction number. This quantity is usually computed using the reported number of cases, but ignoring that many more individuals may be infected (e.g. asymptomatic carriers). We develop a Bayesian procedure to quantify the impact of undetected infectious cases on the determination of the effective reproduction number. Our approach is stochastic, data-driven and not relying on any compartmental model. It is applied to the COVID-19 outbreak in eight different countries and all Italian regions, showing that the effect of undetected cases leads to estimates of the effective reproduction numbers larger than those obtained only with the reported cases by factors ranging from two to ten.