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Article	R. Schlickeiser, M. Kröger Dark numbers and herd immunity of the first Covid-19 wave and future social interventions Epidem. Int. J. 4 (2020) 000152
The Gauss model for the time evolution of the first corona pandemic wave allows to draw conclusions on the amount of unreported cases per reported case, i.e., .dark number. of infections, the amount of herd immunity, the used maximum capacity of breathing apparati and the effectiveness of various non-pharmaceutical interventions in different countries. In Germany, Switzerland, Sweden, and Austria the dark numbers are 8.4 +/- 4.0, 12.6 +/- 5.8, 21.8 +/- 9.1, and 8.5 +/- 5.2, respectively. Our method of estimating dark numbers from modeling both, infection and death rates simultaneously serves as important benchmark to judge on the completeness of testing large portions of the population. For countries that cannot afford the laborious, timeconsuming and costly testing our method still provides them with a reliable estimate of the fraction of infected persons. In Germany the total number of infected individuals, including the dark number of infections by the first wave is estimated to be 1.6 +/- 0.5 million, corresponding to 1.9±0.6 percent of the German population. We work out direct implications from these predictions for managing the 2nd and further corona waves. for LaTeX users @article{RSchlickeiser2020-4,  author = {R. Schlickeiser and M. Kr\"oger},  title = {Dark numbers and herd immunity of the first Covid-19 wave and future social interventions},  journal = {Epidem. Int. J.},  volume = {4},  pages = {000152},  year = {2020} } \bibitem{RSchlickeiser2020-4} R. Schlickeiser, M. Kr\"oger, Dark numbers and herd immunity of the first Covid-19 wave and future social interventions, Epidem. Int. J. {\bf 4} (2020) 000152. RSchlickeiser2020-4 R. Schlickeiser, M. Kr\"oger Dark numbers and herd immunity of the first Covid-19 wave and future social interventions Epidem. Int. J.,4,2020,000152