Efficient Bayesian inference of Instantaneous Reproduction Numbers at Fine Spatial Scales, with an Application to Mapping and Nowcasting the Covid-19 Epidemic in British Local Authorities

Abstract

information about population flows to model potential transmissions across local areas. A simple approach to posterior simulation quickly becomes computationally infeasible, which is problematic if the system is required to provide timely predictions. We describe how to make posterior simulation for the model efficient, so that we are able to provide daily updates on epidemic developments.The results can be found at our web site https://localcovid.info, which is updated daily to display estimated instantaneous reproduction numbers and predicted case counts for the next weeks, across local authorities in Great Britain. The codebase updating the web site can be found at https://github.com/oxcsml/Rmap. We hope that our methodology and web site will be of interest to researchers, policy-makers and the public alike, to help identify upcoming local outbreaks and to aid in the containment of Covid-19 through both public health measures and personal decisions taken by the general public. DATAOur model is applied to publicly available daily counts of positive test results reported under the combined Pillars 1 (NHS and PHE) and 2 (commercial partners) of the UK's Covid-19 testing strategy. 1 The data are available for 312 lower-tier local authorities (LTLAs) in England, 14 NHS Health Boards in Scotland (each covering multiple local authorities) and 22 unitary local authorities in Wales, for a total of n = 348 local areas. The data are daily counts of lab-confirmed (PCR swab) cases presented by specimen date, starting from 30 January 2020. The original data are from the respective national public health authorities of England 2 , Scotland 3 and Wales 4 and we access them through the DELVE Global Covid-19 Dataset 5 (Bhoopchand et al., 2020). Due to delays in processing tests, we ignore the last 7 days of case counts. METHODOur method is based on an approach to infectious disease modelling using discrete renewal processes. These have a long history, and have served as the basis for a number of recent studies estimating instantaneous reproduction numbers, (Cori et al., 2013;Flaxman et al., 2020;Fraser, 2007; Wallinga & Teunis, 2004). See Bhatt et al. ( 2020) and references therein for historical and mathematical background, as well as Gostic et al. ( 2020) for important practical considerations.Following Flaxman et al. (2020), we model latent time series of incidence rates via renewal processes, and separate observations of reported cases using negative binomial distributions, to account for uncertainties in case reporting, outliers in case counts, and delays between infection and testing. We introduce a number of extensions and differences addressing issues that arise for applications to modelling epidemics at local authority level rather than regional 1 https://www.gov.uk/government/publications/coronavirus-covid-19-scaling-up-testing-programmes 2 https://coronavirus.data.gov.uk 3 https://publichealthscotland.scot/our-areas-of-work/sharing-our-data-and-intelligence/coronavirus-covid-19-dataand-guidance/ 4 https://phw.nhs.wal...

Combining models to generate a consensus effective reproduction numberRfor the COVID-19 epidemic status in England

“…Oxford CSML Model Dashboard on [56] Hierarchical semi-mechanistic Bayesian model fitted to cases, similar to Epidemia and as described in [33], but with a spatio-temporal component R is derived using the renewal Equation ( 2…”

‘Introduction’

“…They both adopt a renewal equation framework for the epidemic modelling and a Bayesian estimation framework, differing in how they treat the spatial dynamics of transmission. Mishra et al (2022) do not explicitly model spatial dependence between areas, whereas Teh et al (2022) adopt a spatiotemporal hierarchical formulation and resort to some approximations to address the resulting computational issues. The final session returned to the topic of the R-number with a detailed discussion by Pellis et al (2022) of its properties and of the statistical issues faced for its estimation as the underlying model is progressively complexified.…”

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

“…Simulation results, however, will necessarily depend on which model is used to generate data, and it is unclear to what degree they translate to the real world. It has been argued that R t estimates can be evaluated based on derived short-term forecasts (Teh et al, 2022); this, however, is challenging as e.g., errors in the estimated R t and the assumed generation time distribution may cancel out so that even bad R t estimates can yield acceptable forecasts. In this work, we take a complementary approach to simulation and forecasting studies by describing discrepancies between real-world R t estimates and relating them to underlying analytical choices.…”