Example 2: Corona pandemic

Of course, it makes sense to use the current data on the corona pandemic for logistic regression. I took   the data for Germany from the Johns Hopkins University (JHU) website, which is updated daily , and saved it in two CSV files. One, JHU_DE_Mrz.csv,   contains the data for March 2020, the second JHU_DE_Mrz-Apr.csv  I continued to maintain.

Data from: "JHU_DE_Mrz.csv"

Saturation limit:  56 Mio
      Dark figure:  1

ƒ(x) = —————————————————
           162,29 + 5,6000·107 · e^(-0,21846·t)  

Inflection point W(58,37/28 Mio)

Maximum growth rate f'(xw) = 3,0584 Mio

31 Values 
Coeff.of determin.   = 0,97570783
Correlation coeff.    = 0,98777924
Standard deviation = 0,31876448

  Dates from March 1st, 2020 to March 31st, 2020

Data from:  "JHU_DE_Mrz-Apr.csv"

Saturation limit:  56 Mio
     Dark figure:  1

ƒ(x) = —————————————————
           814,09 + 5,5999·107 · e^(-0,11206·t)  

Inflection point W(99,4/28 Mio)

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

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

  Dates from March 1st, 2020 to April 22nd, 2020

I assumed 56 million as the saturation limit. That is 70% of 80 million, the case of alleged herd immunity .

The comparison of the two results thus obtained shows how the dampening measures seems to flatten the logistic function curve and, above all, how the turning point W (tw | f(tw))  of the curve shifts backwards and the maximum number of new infections per day f '(tw)  gets smaller.
If all dampening measures had been abandoned on April 23, 2020, the new infections would have risen faster and faster according to this model and would have reached their maximum on the 88th day, May 27, 2020 with 1.8 million new infections in one day. However, it should be noted that the model is very simplified. Nevertheless, trends can be seen.