[math-fun] 99.9% solution of SIR equations

I asked the question: to what extent is the logistic iteration, x_{n+1} = x_n + x_n*(1-x_n)*dt, a solution of the SIR equations, S' = -S*I, I' = S*I - r*I? The answer, apparently, is 99.9% when dt in [1/10,1], as is shown in the following plots: https://0x0.st/iQv6.png , where the red points are from the discrete iteration and the blue curve is from the continuous ODE solution. The particular function from dt -> r can be found by minimizing err = abs[I' - (S*I - r*I)], after eliminating S by S = Exp[-Int(I*dt)], and after accounting for the non-zero asymptote of S. One shape parameter is one shape parameter, whether it is "dt" or "r", doesn't seem to matter very much at all. --Brad