Modelling daily infections with Covid-19 in Germany, France, and Sweden with a trend line based on day-to-day reproduction rates

The number of persons daily infected with Covid-19 as a function of time is fitted with a trend line based on an iterative power law (n = ¼) with a day-to-day reproduction rate modelled with a polyline. From the trend line, an effective reproduction rate R_eff of Covid-19 is calculated. In all three states, R_eff decreases in the initial phase to one indicating that there is no exponential growth. In Sweden, a steady state with R_eff around 1 and a high daily infection rates. In Germany, R_eff = 1 is reached before public and private life is restricted. With these restrictions, R_eff is reduced further to 0.87 (CI95 [0.83.; 0.91]) after 40 days so that, speculatively estimated, 9500 premature fatalities within two months may have been avoided. In France, it seems that only strongly restricting private life sends R_eff down to 1 and further down to about 0.7 (CI95 [0.3; 1.1]) after 45 days. With R_eff permanently below 1, an exponential decline of the number of daily infections is observed in Germany and France.