A calibration of nucleic acid (PCR) by antibody (IgG) tests in Germany: the course of SARS-CoV-2 infections estimated

In Germany, a consortium of authority-accredited laboratories (ALM) covered approximately 90% of all severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) polymerase chain reaction (PCR) tests during the COVID-19 pandemic (March 2020 until January 2023), and they likewise conducted serological mass tests for IgG antibodies until May 2021. We analyzed the ALM-observed week-resolved time courses of test-positive fractions of PCR and IgG tests, by least-squares fitting a simple function of the former to the course of the latter. Specifically, we show that scaling and shifting the cumulative sum of previous PCR-positive fractions effectively reproduces the time course of the IgG-positive fraction. The value of 0.14 found for the fitted scaling parameter means that only 14% of those who were tested PCR-positively actually became infected with SARS-CoV-2. This parameter fit further implies that a quarter of the German population already carried IgG antibodies from natural infections in their blood at the turn of the year from 2020 to 2021. To check this fit using a second, independent analysis, we took from the literature the Germany-specific ratio of 1:10 for the ratio between one positive PCR test and the corresponding number of persons actually infected with SARS-CoV-2, and therewith estimated the time course of the latter within the German population. The courses of all three fractions, i.e., both the observed and the fit-estimated IgG-positives and the fit-estimated infected, matched each other well in the period from early December 2020 to May 2021. The extrapolated courses of both the fit-estimated fractions, i.e., those of the IgG-positives and the infected, align well to perfectly with the IgG-positive fraction (92%) reported by the Robert Koch Institute at the end of 2021.