Fig. 3

Daily reproduction number variations with time for 11 different countries during the period from Jan 20, 2020, up to July 18, 2020. The daily reproduction number, Rd0, is the number, during certain day, of the new cases infected by an early contagious individual. R_d0 equals [I(t)/T]_max: T_max is the time necessary that the wave attains its summit; I(t)_max is the summit value. The median reproduction number R₀ is the mathematical average of R_d0 from onset value down to the minimum value of R_d0. A Shows the time variation of R_d0. One notices that R_d0 declines exponentially from high values down to zero. We calculated (after Eq. 6) the daily reproduction number R_d0 in eleven different countries as shown in A. As seen, R_d0 decreases exponentially with time from high values (at the onset days) down to minimum values when reaching the maximum point of the wave. At this maximum point, R_d0 tends to zero and infections decline down. The inset in A shows the linear behaviour of ln(R_d0) as a function of time that confirms the exponential decrease of R_d0 with time. B Shows the median reproduction number R₀ of 20 different countries. We have estimated the mean value of R₀ after Eq. (7). B Shows the median reproduction number R₀ for 20 different countries. C Confirms the exponential decline of R_d0 as a function of time; the black line represents R_d0 plotted in linear scale while the red line is plotted in logarithmic scale. D Shows the first derivative of the daily infection equation (blue line) and the entire wave is plotted in red. One can notice that the summit of the wave corresponds to the inflection point of the blue curve