One of the key indicators used in tracking the evolution of an infectious disease isthe reproduction number. This quantity is usually computed using the reportednumber of cases, but ignoring that many more individuals may be infected (e.g.asymptomatics). We propose a statistical procedure to quantify the impact of un-detected infectious cases on the determination of the effective reproduction number. Our approach is stochastic, data-driven and not relying on any compartmentalmodel. It is applied to the COVID-19 case in eight different countries and all Italianregions, 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. Our findings urge caution about deciding when and how to relax containment measures based on the value of the reproduction number.
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