One needs a set of 5 parameters such as N, I0, S0, r, and a to do the influenza curve fit. Since N=763 is given and I0 can be taken to be roughly the value for the 1st data point we are left with 3 unknowns for a rough fit. If the data includes the peak of the Infected values we can use it and a formula for Imax in terms of the other unknowns to get an estimate for S0. We are then left with just 2 unknowns needed to make a rough estimate of the parameters which we will take to be r and ρ=a/r.
Given an estimate for Imax one can compute an table of values for S0(ρ), then fit a quadratic curve to the data from the table and use the quadratic to interpolate the data for an assumed value of ρ to estimate S0.
Once a rough estimate is made one can adjust the set of 4 parameters to give a minimum value for the rms error.
The value of "δI rms err" is the rms error for the difference between I(fit) and I(formula). I added a switch to the spreadsheet to allow a comparison with a 1st order numerical integration.
The 2nd order calculation is definitely better.
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