[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]. / Ein mathematisches Modell zur Schätzung der Dunkelziffer von SARS-CoV-2-Infektionen in der Frühphase der Pandemie am Beispiel Deutschland und Italien.

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. AIM: The 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.

[The contribution of epidemiological models to the description of the outbreak of the COVID-19 pandemic]. / Der Beitrag von epidemiologischen Modellen zur Beschreibung des Ausbruchsgeschehens der COVID-19-Pandemie.

After the global outbreak of the COVID-19 pandemic, an infection dynamic of immense extent developed. Since then, numerous measures have been taken to bring the infection under control. This was very successful in the spring of 2020, while the number of infections rose sharply the following autumn. To predict the occurrence of infections, epidemiological models are used. These are in principle a very valuable tool in pandemic management. However, they still partly need to be based on assumptions regarding the transmission routes and possible drivers of the infection dynamics. Despite numerous individual approaches, systematic epidemiological data are still lacking with which, for example, the effectiveness of individual measures could be quantified. Such information generated in studies is needed to enable reliable predictions regarding the further course of the pandemic. Thereby, the complexity of the models could develop hand in hand with the complexity of the available data. In this article, after delineating two basic classes of models, the contribution of epidemiological models to the assessment of various central aspects of the pandemic, such as the reproduction rate, the number of unreported cases, infection fatality rate, and the consideration of regionality, is shown. Subsequently, the use of the models to quantify the impact of measures and the effects of the "test-trace-isolate" strategy is described. In the concluding discussion, the limitations of such modelling approaches are juxtaposed with their advantages.