Estimation of reproduction numbers in real time: Conceptual and statistical challenges

JUNIPER Consortium

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6 Citations (Scopus)


The reproduction number (Formula presented.) has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of (Formula presented.), the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating (Formula presented.) becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Original languageEnglish
Pages (from-to)S112-S130
JournalJournal of the Royal Statistical Society. Series A: Statistics in Society
Issue numberS1
Publication statusPublished - Nov 2022

Bibliographical note

Funding Information:
information Alan Turing Institute, Alexander von Humboldt-Stiftung, Economic and Social Research Council, Engineering and Physical Sciences Research Council, Grant/Award Numbers: EP/N510129/1; EP/V027468/1; EP/V051555/1; Medical Research Council, Grant/Award Numbers: MC UU 00002/11; MC/PC/19067; MR/V028456/1; MR/V038613/1; National Institute for Health Research, National Institute for Health Research Health Protection Research Unit, Grant/Award Number: NIHR200877; Royal Society, Grant/Award Number: INF∖R2∖180067; Wellcome Trust, Grant/Award Number: 202562/Z/16/ZThe authors are very grateful to Phillippa Spencer and the Defence Science and Technology Laboratory (DSTL) data provision team for the relentless data management and provision throughout the pandemic, which has been essential for real-time reproduction number and growth rate estimates.

Publisher Copyright:
© 2022 The Authors. Journal of the Royal Statistical Society: Series A (Statistics in Society) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society.


  • growth rate
  • real-time estimation
  • reproduction numbers


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