Data & Methods
We aim to reliably estimate the instantaneous reproduction number $R_t$ across local authorities in the UK with appropriately quantified uncertainties.
We use publicly available Pillar 1+2 daily counts of positive PCR swab tests by specimen date, for:
- 312 lower-tier local authorities (LTLA) in England (here),
- 14 NHS Health Board level in Scotland (each covering multiple local authorities) (here), and
- 22 Unitary local authorities in Wales (here).
Other data sources:
Specific extensions that we have employed to adapt the renewal equation approach to our local-level model:
- Correlations in effective $R_t$ across neighbouring local authorities and across neighbouring points in time are modelled using a spatio-temporal Gaussian process. This allows for sharing of statistical strengths.
- Potential infections that cross local authority boundaries are accounted for using a cross-coupled metapopulation approach. In order to do so, we incorporate real commuter data from the UK 2011 Census (here).
- Problems associated with noise in the case reporting process, outliers in case counts and delays in the testing and reporting system are alleviated by modelling the epidemic using a latent process with associated observation model for reported cases, following Flaxman et al (2020).
- We use the No-U-Turn Sampler inplemented in the Stan probabilistic programming system for posterior inference.
- Because of the computational cost of posterior simulation in the resulting complex model, we split the posterior simulation into two phases: an initial phase which infers the latent epidemic process in each local authority, and a second phase which infers the $R_t$ and metapopulation model parameters.
Detailed description of the method and source code will be provided as soon as possible.