Estimation of the effective reproductive numberR_tis important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are usingR_tto assess the effectiveness of interventions and to inform policy. However, estimation ofR_tfrom available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation ofR_t, we recommend the approach of Cori and colleagues, which uses data from before timetand empirical estimates of the distribution of time between infections. Methods that require data from after timet, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resultingR_testimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems inR_testimation.

Significance: We estimate the origin and spread of SARS-CoV-2 in Europe prior to spring 2020 border closures based on viral genome sequences using a phylodynamic model with geographic structure. We confirm that the predominant European outbreak most likely started in Italy and spread from there. This outbreak was probably seeded by a transmission event in either Hubei, China or Germany. In particular, we find that before the first border closures in Europe, the rate of new cases occurring from within-country transmission was within or exceeded the estimated bounds on the rate of new migration cases.

Estimation of the effective reproductive number, R _t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R _t to assess the effectiveness of interventions and to inform policy. However, estimation of R _t from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of R _t , we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t , such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R _t estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in R _t estimation. Author summary: The effective reproductive number, R _t , is a key epidemic parameter used to assess whether an epidemic is growing, shrinking or holding steady. R _t estimates can be used as a near real-time indicator of epidemic growth or to assess the effectiveness of interventions. But due to delays between infection and case observation, estimating R _t in near real-time, and correctly inferring the timing of changes in R _t is challenging. Here, we provide an overview of challenges and best practices for accurate, timely R _t estimation.

Background: Accurate estimation of the effective reproductive number ( $$R_e$$Re ) of epidemic outbreaks is of central relevance to public health policy and decision making. We present estimateR, an R package for the estimation of the reproductive number through time from delayed observations of infection events. Such delayed observations include confirmed cases, hospitalizations or deaths. The package implements the methodology of Huisman et al. but modularizes the $$R_e$$Re estimation procedure to allow easy implementation of new alternatives to the currently available methods. Users can tailor their analyses according to their particular use case by choosing among implemented options.Results: The estimateR R package allows users to estimate the effective reproductive number of an epidemic outbreak based on observed cases, hospitalization, death or any other type of event documenting past infections, in a fast and timely fashion. We validated the implementation with a simulation study: estimateR yielded estimates comparable to alternative publicly available methods while being around two orders of magnitude faster. We then applied estimateR to empirical case-confirmation incidence data for COVID-19 in nine countries and for dengue fever in Brazil; in parallel, estimateR is already being applied (i) to SARS-CoV-2 measurements in wastewater data and (ii) to study influenza transmission based on wastewater and clinical data in other studies. In summary, this R package provides a fast and flexible implementation to estimate the effective reproductive number for various diseases and datasets.Conclusions: The estimateR R package is a modular and extendable tool designed for outbreak surveillance and retrospective outbreak investigation. It extends the method developed for COVID-19 by Huisman et al. and makes it available for a variety of pathogens, outbreak scenarios, and observation types. Estimates obtained with estimateR can be interpreted directly or used to inform more complex epidemic models (e.g. for forecasting) on the value of $$R_e$$Re .

The effective reproductive number, Re, is a critical indicator to monitor disease dynamics, inform regional and national policies, and estimate the effectiveness of interventions. It describes the average number of new infections caused by a single infectious person through time. To date, Re estimates are based on clinical data such as observed cases, hospitalizations, and/or deaths. Here we show that the dynamics of SARS-CoV-2 RNA in wastewater can be used to estimate Re in near real-time, independent of clinical data and without associated biases stemming from clinical testing and reporting strategies. The method to estimate Re from wastewater is robust and applicable to data from different countries and wastewater matrices. The resulting estimates are as similar to the Re estimates from case report data as Re estimates based on observed cases, hospitalizations, and deaths are among each other. We further provide details on the effect of sampling frequency and the shedding load distribution on the ability to infer Re. To our knowledge, this is the first time Re has been estimated from wastewater. This method provides a low cost, rapid, and independent way to inform SARS-CoV-2 monitoring during the ongoing pandemic and is applicable to future wastewater-based epidemiology targeting other pathogens. Significance statement The effective reproductive number, Re, is widely used during the COVID-19 pandemic to track disease dynamics, inform regional and national policies, and estimate the effectiveness of interventions. Re is typically estimated from clinical case data, and can be biased by e.g. changes in testing and reporting. We show longitudinal measurements of SARS-CoV-2 RNA in wastewater can be used to estimate Re, across different regions, and provide an independent assessment of the dynamics of COVID-19. Given widespread wastewater sampling during this pandemic, these Re estimates are directly applicable as a rapid, low-cost method to inform public health policy. The method can be adapted to other pathogens, including those for which clinical data is not available.