It seems we've reached the point where it would be advantageous to look at possible errors. If one includes the number of deaths with the number of cases in K one gets similar results with the fit coefficients slightly altered.
The plot of I-S* shows segments that are approximately constant. Note that the peak is about 75 days after the initial date which is 4/1/20. There appears to be more fluctuation due to larger numbers about this time which show up in the plot. There's a drop in the difference after the peak and one can speculate on its cause. Is it due to social distancing? Or maybe there were more cases that were overlooked due to less testing early on? Or could there be something like a Doppler effect with a higher value as the number of cases increases and a lower number as they decrease? A fit error could also be a possible explanation for some of the difference. One could also speculate on how much observation error there is and whether or not the constant of integration, A, is zero or not with I being a possible measure of the number of susceptibles.
The parameter a is the rate at which the infectives become removed so there's a flow of cases through I that does not show up in the statistics and the lower value for S* may reflect this since not all of the I=dK/dt are infectious. This might account for some of the difference.
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