estimateR: An R package to estimate and monitor the effective reproductive number (preprint)

Background The accurate estimation of the effective reproductive number (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 may for example be confirmed cases, hospitalizations or deaths. The Re estimation procedure is modularized which allows easy implementation of new alternatives to the already-available methods. Users can tailor their analyses according to their particular use cases by choosing among implemented variations. The package is based on the methodology of Huisman et al., developed as a response to the COVID-19 pandemic. 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, and by comparing results from estimateR to results from the Huisman et al. pipeline on empirical COVID-19 case-confirmation incidence. Compared to existing methods, estimateR implements unique features whose benefit we demonstrated with a simulation study. On simulated data, estimateR yielded estimates of similar, if not better, accuracy than compared alternative publicly available methods while being two to three orders of magnitude faster. 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 extendible 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 Re.

Wastewater-based estimation of the effective reproductive number of SARS-CoV-2 (preprint)

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.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2 (preprint)

The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the SARS-CoV-2 pandemic started, many methods and online dashboards have sprung up to monitor this number. However, these methods are not always thoroughly tested or are applied only to a limited geographic range. Here, we present a method for near real time monitoring of Re, applied to epidemic data from 170 countries. We thoroughly validate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe, Asia, and North America we found that the implementation of non-pharmaceutical interventions was associated with reductions in the effective reproductive number. Globally, we found that relaxing non-pharmaceutical interventions did not fully revert Re values to their original levels. Generally, our framework is useful both to inform governments and the general public on the status of the epidemic in their country, as well as a source for detailed comparison between countries and in relation to local public health policies and external covariates such as mobility, behavioural, or weather data.

Estimates of outbreak-specific SARS-CoV-2 epidemiological parameters from genomic data (preprint)

We estimate the basic reproductive number and case counts for 15 distinct SARS-CoV-2 outbreaks, distributed across 10 countries and one cruise ship, based solely on phylodynamic analyses of genomic data. Our results indicate that, prior to significant public health interventions, the reproductive numbers for a majority (10) of these outbreaks are similar, with median posterior estimates ranging between 1.4 and 2.8. These estimates provide a view which is complementary to that provided by those based on traditional line listing data. The genomic-based view is arguably less susceptible to biases resulting from differences in testing protocols, testing intensity, and import of cases into the community of interest. In the analyses reported here, the genomic data primarily provides information regarding which samples belong to a particular outbreak. We observe that once these outbreaks are identified, the sampling dates carry the majority of the information regarding the reproductive number. Finally, we provide genome-based estimates of the cumulative case counts for each outbreak, which allow us to speculate on the amount of unreported infections within the populations housing each outbreak. These results indicate that for the majority (7) of the populations studied, the number of recorded cases is much bigger than the estimated cumulative case counts, suggesting the presence of unsequenced pathogen diversity in these populations.

Practical considerations for measuring the effective reproductive number, Rt (preprint)

Estimation of the effective reproductive number, Rt, is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt 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 methodological recommendations. For near real-time estimation of Rt, 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 some retrospective analyses. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. A challenge common to all approaches is 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 Rt estimation.

The origin and early spread of SARS-CoV-2 in Europe (preprint)

The investigation of migratory patterns of the SARS-CoV-2 pandemic before border closures in Europe is a crucial first step towards an in-depth evaluation of border closure policies. Here we analyze viral genome sequences using a phylodynamic model with geographic structure to estimate the origin and spread of SARS-CoV-2 in Europe prior to border closures. Based on SARS-CoV-2 genomes, we reconstruct a partial transmission tree of the early pandemic, including inferences of the geographic location of ancestral lineages and the number of migration events into and between European regions. We find that the predominant lineage spreading in Europe has a most recent common ancestor in Italy and was probably seeded by a transmission event in either Hubei or Germany. We do not find evidence for preferential migration paths from Hubei into different European regions or from each European region to the others. Sustained local transmission is first evident in Italy and then shortly thereafter in the other European regions considered. Before the first border closures in Europe, we estimate that the rate of occurrence of new cases from within-country transmission was within the bounds of the estimated rate of new cases from migration. In summary, our analysis offers a view on the early state of the epidemic in Europe and on migration patterns of the virus before border closures. This information will enable further study of the necessity and timeliness of border closures.