Bertalanffy-Pütter models for the first wave of the COVID-19 outbreak.

The COVID-19 pandemics challenges governments across the world. To develop adequate responses, they need accurate models for the spread of the disease. Using least squares, we fitted Bertalanffy-Pütter (BP) trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed. BP-models achieved excellent fits (R-squared above 99%) to all data. Using them to smoothen the data, in the median one could forecast that the final count (asymptotic limit) of infections and fatalities would be 2.48 times (95% confidence limits 2.42-2.6) and 2.67 times (2.39-2.765) the total count at the respective peak (inflection point). By comparison, using logistic growth would evaluate this ratio as 2.00 for all data. The case fatality rate, defined as the quotient of the asymptotic limits of fatalities and confirmed infections, was in the median 4.85% (confidence limits 4.4%-6.5%). Our result supports the strategies of governments that kept the epidemic peak low, as then in the median fewer infections and fewer fatalities could be expected.