The reproductive number, Rt, is a widely used metric for tracking infectious disease dynamics, describing the expected number of infections caused by a single case at time t. While Rt has existed for decades, its use expanded dramatically during the COVID-19 pandemic, leading to a rapid proliferation of estimation methods and software tools. This growth has created both opportunities and challenges for researchers, practitioners, and decision makers, as it is not clear which tool to use for which analytical goals.
To address these issues, we convened the Epistorm Rt-Estimate Collabathon in September 2024, bringing together researchers and public health professionals to identify key challenges and chart directions for future work. From this effort, we developed two key resources:
• A set of recommendations for improving methods and tools and guiding future development.
• A framework for evaluating and interpreting Rt estimates across different tools.
Together, these contributions aim to support more reliable, interpretable, and actionable use of Rt in public health practice.
• Realtime, data driven estimates of the transmission dynamics of an infectious disease are important to inform public health actions.
• The reproductive number, Rt, equips public health officials with tools to interpret data they are collecting on ongoing and emerging infectious disease threats to understand the current transmission dynamics of the disease.
The instantaneous reproductive number Rt provides a simple summary of the current infectious potential of an infectious disease and provides insight on whether disease case rates are likely to be increasing, decreasing or stay steady in the near term (see right).
Importantly, Rt cannot be measured directly. Instead, Rt is commonly estimated at discrete timepoints using the renewal equation:
which relates Rt to a time-series of incident infections (It) and the generation interval (ω), a vector representing the distribution of time between primary and secondary infection. The term Λt is used to represent the total infectiousness.
Variations in Rt at a given time (represented by the arrow on the x axis), for (A) Rt < 1, where the outbreak is shrinking, (B) Rt = 1, where the outbreak is stable, or (C) Rt> 1, where the outbreak is growing. The shaded pink area shows the confidence interval on the estimate of Rt.
Illustration of a schematic pipeline of this process highlighting (A) several common challenges in data formatting and consistency, (B) examples of Rt estimation tools, and (C) some of the many downstream tasks for which Rt estimates are useful.
Many methods that have emerged to estimate Rt use different methodological assumptions that lead to differing values of Rt even if the same inputs are used. The purpose of our work is to provide guidance to public health practitioners as to which Rt estimation tool to choose based on their analytical goals. First, we outline common data types, inputs, and challenges existing in Rt estimation. The figure summarizes many of the challenges, tools and uses of Rt estimation methods.
Our current work focuses on methods to provide more geographically granular estimates of Rt that incorporate mobility patterns and delays in reporting.
To provide a more granular view, we also review each estimation method at a public facing website: https://sites.bu.edu/disease-rt/.
The purpose of this document is to provide guidance about which estimation software to choose for different analytical goals. We provide an RShiny online tool that details the components of an Example outbreak and shows how different components of a disease outbreak can be modeled differently.
We also provide a Decision tool for how to choose software for different analytical goals. For each of these R packages, a separate page details the components of each package and gives some sample R code that can be used to implement each tool in practice.
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