That is interesting and useful information. That is probably a large number of infected people to drop into a healthy population. I would guess the usual outbreak would start with something more like a family size. It may take a while for the numbers to stabilize.
In[]:=
skoreaCases1={#1,#2-31}&@@@Drop[skoreaCases,29]
Out[]=
{{30,73},{31,173},{32,402},{33,571},{34,802},{35,946},{36,1230},{37,1735},{38,2306}}
In[]:=
skoreaNLM1=NonlinearModelFit[skoreaCases1,logistic,{{k,0.3},{L,10000},{t0,50}},t];​​skoreaNLM1["BestFitParameters"]
Out[]=
{k0.349697,L9023.4,t041.0882}
The fits with 95% confidence intervals. By the discussion above the confidence intervals may be underestimated. Clearly no early predictions can be made.
Out[]=
In[]:=
skoreaNLM1@"ParameterConfidenceIntervalTable"
Out[]=
Estimate
Standard Error
Confidence Interval
k
0.349697
0.0620365
{0.197899,0.501495}
L
9023.4
9303.95
{-13742.5,31789.3}
t0
41.0882
4.40935
{30.2989,51.8775}