I doubt if one exponential curve would fit all the data, particularly as people change their behavior in response to the disease (i.e., reducing contacts with others) or if efforts at containment by medical staff or government were even partially successful. Changes like those would affect the number of transmissions to others and slow the growth of cases.
Still, the modeling you are doing is very useful, incomplete data or not. Thank you.
I completely agree.
Indeed, my last plot showed this effect: the curves change because behavior changes.
The intent of the modeling is just as you suggest: it is a guideline, something to give us a feel for the implications of what is happening. Since there is a parametric change, I cannot model this analytically. It has to be done on a computer. However, I don't want to be accused of being one of those "global warming" scientists who create elaborate computer models with little or no data. As you, Eternal Hope, and others have pointed out, I am probably pushing the limit on this given the quality of the data. :-}