Correcting the Reproduction Number for Time-Varying Tests: a Proposal and an Application to COVID-19 in France*

Abstract We provide a novel way to correct the effective reproduction number for the time-varying amount of tests, using the acceleration index as a simple measure of viral spread dynamics (Baunez et al., 2021). Not doing so results in the reproduction number being a biased estimate of viral acceleration and we provide a formal decomposition of the resulting bias, involving the useful notions of test and infectivity intensities. When applied to French data for the COVID-19 pandemic (May 13 - November 19, 2020), our decomposition shows that the reproduction number, when considered alone, consistently underestimates the resurgence of the pandemic since the summer of 2020, compared to the acceleration index which accounts for the time-varying volume of tests. Because the acceleration index aggregates all relevant information and captures in real time the sizable time variation featured by viral circulation, it is a more parsimonious indicator to track the dynamics of an infectious disease outbreak in real time, compared to the equivalent alternative which would be to complement the reproduction number with the test and infectivity intensities.