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

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Birrell, Paul J 
Overton, Christopher E  ORCID logo
Scarabel, Francesca  ORCID logo


The reproduction number R 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 R , 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 R 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.


Funder: Alan Turing Institute; Id:

Funder: Alexander von Humboldt‐Stiftung; Id:

Funder: Economic and Social Research Council; Id:

Funder: National Institute for Health Research; Id:


growth rate, real‐time estimation, reproduction numbers

Journal Title

J R Stat Soc Ser A Stat Soc

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Oxford University Press (OUP)
MRC (via University of Warwick) (MR/V038613/1)