A mathematical model to estimate the number of unreported SARS-CoV-2 infections in the early phase of the pandemic using Germany and Italy as examples

Background Especially in the early phase, it is difficult to obtain reliable figures on the spread of a pandemic. The effects of the COVID-19 pandemic and the associated comprehensive but incomplete data monitoring provide a strong reason to estimate the number of unreported cases.AimThe aim of this paper is to present a simple mathematical model that allows early estimation of the number of unregistered cases (underreporting). Material and methods Prevalences of reported infections in different age groups are combined with additional assumptions on relative contact rates. From this, a corrected prevalence is derived for each age group, which can then be used to estimate the number of unreported cases. Results Our model derives for Germany in mid-April 2020 about 2.8 times more total infections than registered cases. For Italy, the model results in a factor of 8.3. The case mortalities derived from this are 0.98% for Germany and 1.51% for Italy, which are much closer together than the case mortalities of 2.7% and 12.6% derived purely from the number of reports available at that time. Conclusion The number of unreported SARS-CoV-2-infected cases derived from the model can largely explain the difference in observations in case mortalities and of conditions in the early phase of the COVID-19 pandemic in Germany and Italy. The model is simple, fast, and robust to implement, and can respond well when the reporting numbers are not representative of the population in terms of age structure. We suggest considering this model for efficient and early estimations of unreported case numbers in future epidemics and pandemics.