Influence of the dark figure

In the corona pandemic, many virologists assume that the number of infected people is 100 times greater than the number of people tested positive. If you multiplicate all measured values with this factor (dark figure), this has a considerable influence on the curve fitting, since it brings you closer to the saturation limit.

Without dark figure:

Data from:  "JHU_DE_Mrz-Apr.csv"

Saturation limit:  56 Mio
     Dark figure:  1

f(t) = 4,559E10/(814,1 + 5,51E7*e^(-0,112*t))

Inflection point W(99,4/28 Mio)

Maximum growth rate f'(xw) = 1,5688 Mio

60 Values 
Coeff.of determin. = 0,82574762
Correlation coeff. = 0,90870656
Standard deviation = 0,90673232

With dark figure = 100:

Data from:  "JHU_DE_Mrz-Apr.csv"

Saturation limit:  56 Mio
     Dark figure:  100

f(t) = 4,250E12/(75885 + 5,59E7*e^(-0,119*t))

Inflection point W(55,437/28 Mio)

Maximum growth rate f'(xw) = 1,6674 Mio

60 Values 
Coeff.of determin. = 0,8471621
Correlation coeff. = 0,92041409
Standard deviation = 0,89105973

With dark figure = 330:

Data from:  "JHU_DE_Mrz-Apr.csv"

Saturation limit:  56 Mio
     Dark figure:  330

f(t) = 7,82E12/(1,40E5 + 5,59E7*e^(-0,162*t))

Inflection point W(36,931/28 Mio)

Maximum growth rate f'(xw) = 2,2714 Mio

60 Values 
Coeff.of determin. = 0,95628418
Correlation coeff. = 0,97789784
Standard deviation = 0,61100523

The coefficient of determination is obviously highest in the third example and the curve also seems to match the measured values best. However, one always has to ask where the data modeling ends and the data manipulation begins.