New insights into the estimation of reproduction numbers during an epidemic

In this paper, we deal with the problem of estimating the reproduction number R t duringan epidemic, as it represents one of the most used indicators to study and control this phenomenon.In particular, we focus on two issues. First, to estimate R t , we consider the use of positive test casedata as an alternative to the first symptoms data, which are typically used. We both theoreticallyand empirically study the relationship between the two approaches. Second, we modify a methodfor estimating R t during an epidemic that is widely used by public institutions in several countriesworldwide. Our procedure is not affected by the problems deriving from the hypothesis of R t localconstancy, which is assumed in the standard approach. We illustrate the results obtained by applyingthe proposed methodologies to real and simulated SARS-CoV-2 datasets. In both cases, we also applysome specific methods to reduce systematic and random errors affecting the data. Our results showthat the R t during an epidemic can be estimated by using the positive test data, and that our estimatoroutperforms the standard estimator that makes use of the first symptoms data. It is hoped that thetechniques proposed here could help in the study and control of epidemics, particularly the currentSARS-CoV-2 pandemic.