This modelling study from Sweden suggests 26% of Stockholm county will have been infected by May 1st ( https://www.folkhalsomyndigheten.se/contentassets/2da059f90b90458d8454a04955d1697f/skattning-peakdag-antal-infekterade-covid-19-utbrottet-stockholms-lan-februari-april-2020.pdf). However, our estimates of under-reporting suggest only 5-10% have been infected so far ( https://cmmid.github.io/topics/covid19/global_cfr_estimates.html). So what's going on? 1/

The model uses a study that found 2.5% of a random sample tested positive in Stockholm County early April. As only 150–200 cases were being reported each day during that period, it suggests there was a lot more infection out there. But how much exactly? 2/

The key issue here is that the number currently infected (i.e. prevalence) isn't the same as the number of new cases (incidence). To account for this, the model fits to both observed cases and the number infected (i.e. the 2.5% prevalence estimate). And here's the issue... 3/

To work out under-reporting we need to compare that 2.5% to how many active infections were being reported at same point. The model assumes people are infectious for 5 days, i.e. it effectively compares 5d worth of reported cases (i.e. ~800) with the 2.5% prevalence estimate. 4/

This suggests about 70-80 infections for each reported case, which leads to 26% estimate. But are people really infected for only 5d? People may be *infectious* for relatively short period, but they can test +ve for longer: possibly 2 weeks on average https://www.medrxiv.org/content/10.1101/2020.04.05.20053355v2 5/

This suggests we shouldn't be comparing 2.5% with cases over 5 days - we should be looking at the previous 2 weeks. Looks like ~2400 cases were reported during this period, suggesting around 25 infections per reported case. In other words, 1/3 of the value they estimate... 6/

This would imply 5–10% will have been infected by 1 May, consistent with our estimate (and Imperial: https://mrc-ide.github.io/covid19estimates/#/details/Sweden). The above is of course just a rough estimate, but it shows that it's always worth checking results against other data sources. 7/7