I am fascinated by your analysis, even if the last 2 days are not fitting well. So I set up my own Excel doc with your equation.
QUESTIONS:
1) How did you arrive at the asymptotic value of 41,500? I thought we were solving for the max cases ... but now I realize that assumption came from a priori reasoning.
2) Obviously the epidemic hit the U.S. earlier than your current assumption, which places patient “Zero” around March 10th ... whereas there were at least 70 known cased by about March 2nd or so. So I’m thinking March 14 should be more like DAY 15 in the growth equation.
3) Can you give me some insight where the other 2 parameters in the exponent came from?
4) I get a better fit to the data, especially today’s totals, using March 14th as day 15, setting the MAX CASES=500,000; resetting your .1988 factor to .2754311; and resetting your 3.2392 factor to 9.0.
Even so, this assumes there was a degree of under-testing until the last 2 days.
NOTES:
500,000 confirmed cases (if that were the number) would certainly not overwhelm the health system, and would probably result in just few thousand deaths, allowing POTUS to declare victory.
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It is conceivable the Trillion-Dollar BAILOUT CHECKS ALONE could cost about $1 billion per death.
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Someday we will truly understand the growth function of this virus, and be able to assess the magnitude of the (over)reaction versus what we could have legitimately faced with normal safeguards like washing hands and quarantining actual cases.
1+2) I got 41500 by extrapolating the Hubei confirmed case growth rates from 1/30 on the US confirmed case counts circa 3/10. Clearly, that was an error. In retrospect, I picked the wrong Hubei starting date; the recent fit is much better if I indexed the growth rate starting from 1/24 in Hubei. If I reset the growth rats like I said in #1, the US case count forecast grows to about 181k.
3)I eyeballed the growth rates to build a data set of high and low growth flags by date, and modeled a logistic function. There are several 'free' ones online. Since I modeled growth rates vs the actual counts I didn't have to correct for autocorrelation in the data.
I can, of course, 'fix' the model but I'm a man of my word. Once this thing becomes way bad I can reset the forecast. Besides, I've already posted my forecast so it's all transparent.