Calculating the number of undetected active SARS-CoV-2 infections from results of population-wide antigen tests

Current European research estimates the number of undetected active SARS-CoV-2 infections (dark figure) to be two- to 130-fold the number of detected cases. We revisited the population-wide antigen tests in Slovakia and South Tyrol and calculated the dark figure of active cases in the vulnerable populations and the number of undetected active cases per detected active case at the time of the population-wide tests. Our analysis follows three steps: using the sensitivities and specificities of the used antigen tests, we first calculated the number of test-positive individuals and the proportion of actual positives in those who participated in the antigen tests. We then calculated the dark figure in the total population of Slovakia and South Tyrol, respectively. Finally, we calculated the ratio of the dark figure in the vulnerable population to the number of newly detected infections through PCR tests. Per one positive PCR result, another 0.15 to 0.71 cases must be added in South Tyrol and 0.01 to 1.25 cases in Slovakia. The dark figure was in both countries lower than assumed by earlier studies.