Fitting the reproduction number from UK coronavirus case data and why it is close to 1

  1. Graeme J. Ackland
  2. James A. Ackland
  3. Mario Antonioletti
  4. David J. Wallace

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Abstract

We present a method for rapid calculation of coronavirus growth rates and R -numbers tailored to publicly available UK data. We assume that the case data comprise a smooth, underlying trend which is differentiable, plus systematic errors and a non-differentiable noise term, and use bespoke data processing to remove systematic errors and noise. The approach is designed to prioritize up-to-date estimates. Our method is validated against published consensus R -numbers from the UK government and is shown to produce comparable results two weeks earlier. The case-driven approach is combined with weight–shift–scale methods to monitor trends in the epidemic and for medium-term predictions. Using case-fatality ratios, we create a narrative for trends in the UK epidemic: increased infectiousness of the B1.117 (Alpha) variant, and the effectiveness of vaccination in reducing severity of infection. For longer-term future scenarios, we base future R ( t ) on insight from localized spread models, which show R ( t ) going asymptotically to 1 after a transient, regardless of how large the R transient is. This accords with short-lived peaks observed in case data. These cannot be explained by a well-mixed model and are suggestive of spread on a localized network.

This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

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  1. Version published to 10.1098/rsta.2021.0301
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  3. Version published to 10.1101/2021.09.23.21256065v1 on medRxiv