Daily cases can be falling while the number of people infected still rises

At present, confirmed cases in the UK are declining; by specimen date in England, they fell by 29% in the week up to 24 July. In contrast, the Office for National Statistics (ONS) estimates that over the same period the proportion of the population in England infected with SARS-CoV-2 continued to rise, to around 1 in 60. Is there a conflict between these trends?

The measures are somewhat different: testing data provides new recorded infections (the incidence); Public Health England counts some positives from rapid tests, as well as standard PCR tests. The ONS results are based on its large infection survey: a nationally representative sample is repeatedly PCR-tested for the virus and so estimates how many people would currently test positive (the positivity).

But people with the virus can test positive for many days. Think of it like filling a bath with the plughole open. Incidence is how quickly water flows in, the positivity is the level of the water in the bath, and there is some draining as older infections fall away. As you start turning the taps down, the level continues to rise for a while longer, until the plughole takes over.

This is demonstrated in Scotland, which has been ahead of England both in starting school holidays and getting knocked out of Euro 2020. Its confirmed cases hit a peak at the end of June and central ONS positivity estimates and hospitalisations are now declining. This is all good, and somewhat unexpected, news.

Other recent survey findings include that 40% of infections show no symptoms - a bit higher than the “one in three” figure usually quoted. And for those unlucky enough to get reinfected, at least the second infection tends to be milder. In contrast, the US struggles without a nationwide survey and so has only now estimated that 60% of infections have gone unreported.

The daily-updated PHE dashboard and the ONS Covid Infection Survey are excellent and complementary resources (but note that David Spiegelhalter chairs the survey’s advisory board, so he would say that, wouldn’t he?). Different data sources form a mosaic of evidence and insight.

• David Spiegelhalter is chair of the Winton Centre for Risk and Evidence Communication at Cambridge. Anthony Masters is statistical ambassador for the Royal Statistical Society