  The number of new infections per day is a key quantity for effective epidemic
management. It can be estimated relatively directly by testing of random
population samples. Without such direct epidemiological measurement, other
approaches are required to infer whether the number of new cases is likely to
be increasing or decreasing: for example, estimating the pathogen effective
reproduction number, R, using data gathered from the clinical response to the
disease. For Covid-19 (SARS-CoV-2) such R estimation is heavily dependent on
modelling assumptions, because the available clinical case data are
opportunistic observational data subject to severe temporal confounding. Given
this difficulty it is useful to retrospectively reconstruct the time course of
infections from the least compromised available data, using minimal prior
assumptions. A Bayesian inverse problem approach applied to UK data on first
wave Covid-19 deaths and the disease duration distribution suggests that fatal
infections were in decline before full UK lockdown (24 March 2020), and that
fatal infections in Sweden started to decline only a day or two later. An
analysis of UK data using the model of Flaxman et al. (2020, Nature 584) gives
the same result under relaxation of its prior assumptions on R, suggesting an
enhanced role for non pharmaceutical interventions (NPIs) short of full lock
down in the UK context. Similar patterns appear to have occurred in the
subsequent two lockdowns. Estimates from the main UK Covid statistical
surveillance surveys, available since original publication, support these
results. Replication code for the paper is available in the supporting
information of doi/10.1111/biom.13462.
