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

Ackland, G. J.; Ackland, J. A.; Antonioletti, M.; Wallace, D. J.

We present a method for rapid calculation of coronavirus growth rates and R-numbers tailored to the publicly available data in the UK. The R-number is derived from time-series of case data, using bespoke data processing to remove systematic and errors and stochastic fluctuations. In principle, growth rate can be obtained by differentiating the reported case numbers, but in fact daily stochastic fluctuations disqualify this method. We therefore assume that the case data comprises a smooth, underlying trend which is differentiable and a noise term. The approach produces, up-to-date estimates of the R-number throughout the period of data availability. Our method is validated against published consensus R-numbers from the UK government, and shown to produce comparable results. A significant advantage of our method is that it is stable up to the most recent data, this enables us to make R-number estimates available over two weeks ahead of the published consensus. The short-lived peaks observed in the R-number and case data cannot be explained by a well-mixed model and are suggestive of spread on a localised network. Such a localised spread model tends to give an Rt number close to 1, regardless of how large R0. The case-driven approach is combined with Weight-Shift-Scale (WSS) 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 alpha and delta variants, and the effectiveness of vaccination in reducing severity of infection.