Extended Data Fig. 1: Longitudinal model DAG for SIR epidemic model at local level (for example LTLA).

Directed paths characterise conditional probability distributions, in contrast to the paths showing transitions between model compartments in Supplementary Fig. 1. Inference is for a region, for example an LTLA, based only on targeted test data collected in this region, n_t of N_t. A prior on δ_t parameterized (\({\hat{\mu }}_{t}\), \({\hat{\sigma }}_{t}^{2}\)) brings information on the Pillar 1+2 ascertainment bias learned from randomized surveillance testing data available for the PHE region in which the LTLA lies. The T × T covariance matrix Σ_δ imparts temporal smoothness on δ_1:T. Effective reproduction numbers are denoted \({{{{\mathcal{R}}}}}_{1:T}\), number of infectious individuals by I_1:T, and the number of immune individuals by \({R}_{1:T}^{+}\).