What you saw was what you got? Correcting reported incidence data for testing intensity

During the COVID-19 pandemic, non-pharmaceutical interventions were employed to limit the spread of the SARS-CoV-2 virus. In some countries, this included large-scale voluntary testing of non-symptomatic individuals to gauge the prevalence in the general population and to identify asymptomatic and pre-symptomatic infections in order to reduce disease spread. Differences between the intensity of testing means that comparing case-counts across borders may be deceptive. In this work, we use mathematical modeling to investigate the dynamics of both observed and unobserved infections as a function of the rate of voluntary testing. The model indicates that increasing the rate of testing causes the number of observed cases to increase, despite a decrease in prevalence due to testing. For large testing rates, the observed case-counts also decrease. The non-monotonicity of the observed cases explains some discrepancies seen when comparing uncorrected case-counts between countries. One such example was observed during the winter 2020/2021 COVID-19 epidemics in Denmark and Hungary, where reported case-counts were comparable, despite differences in prevalence. We determine a quantitative measure for the ascertainment ratio between observed cases and all infections, allowing for test-intensity correction of case-counts. This measure allows us to correct case-counts for testing intensity during the winter 2021/2022 epidemic of the Omicron variant (BA.1 and BA.2) in Denmark, showing good agreement with results from serology-studies. While the model does not capture the full complexity of epidemic dynamics, it provides a simple way to correct case-counts for differences in testing, simplifying comparison across international borders and testing activities.