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# [Phys-L] Confessions of a Repentant Modeler in a Time of Plague.

It has been a wild ride.
I began with exponential fits - which worked quite well
for Oklahoma until they didn't. Then I swung over to straight-line fits until, as it seemed to me, the new day hits were all on the low side. So what else but a logistic fit.
Mea Culpa!
I used a logistic form that concealed even the time value of the peak rate instead of the infinitely more sensible standard form used by bc when he tried this fit for Andorra.(note 1)

When I shared these plots with others, I noted a certain rolling of the eyes, concerning their simplicity - but I persisted, until I finally realized my exponential fits were getting daily hits on the upside: not from a data uptrend, but from the logistic curve downtrend in face of a continued straight line fit.
So I retreated from the simple three factor fit, to the simpler two factor straight line fit, whence I should not have too eagerly jumped. My data source was Note 2.
Here are some comparisons of the [accumulated] US CASES time series, as a straight line (which fits well) or a logistic, which is trying its best.
https://imgur.com/pcj4yR0 US CASES LINEAR
https://imgur.com/YKCgfYP US CASES LOGISTIC

For comparison, here is a rate projection by a commercial  source:
https://imgur.com/pekQmWH MORGAN-STANLEY FORECAST

Onto plots of US deaths:
You can easily see the linear plot for Deaths is concave up in data.
https://imgur.com/e7uhJVf US DEATH LIN

Here, an exponential or even logistic curve fits the facts better.
https://imgur.com/EfXprh0 US DEATH LOG

Though of less general interest, I offer the Oklahoma plots below, where The straight line plots fit the facts for recent Cases and Deaths, and the logistic is betrayed by the upside departures of the data.
https://imgur.com/bMVsB0v OK DEATH LOGISTIC
https://imgur.com/sE0zP3G OK DEATH LINEAR

https://imgur.com/Kzsr1rW OK CASES LOGISTIC
https://imgur.com/9UAKU0b OK CASES LINEAR

Finally, an academic forecast for Oklahoma from IMHE.

Search Results

IMHE is the Institute for Health Metrics & Evaluation at U Washington-Medicine - a source favored by President Trump.

https://imgur.com/GLdSIf3 IHME FORECAST (OKLAHOMA)

Compare the timid US resources forecast from that source for ventilators - which correlates with US Deaths - as most CV-19 patients on that device do not emerge alive.
https://covid19.healthdata.org/united-states-of-america

The purple and gray shading represents their uncertainty!

Brian W

Note 1) I initially used the logistic form
(plateau level) /(1 + exp(a - b*t)

Instead of the better form used by bc
(plateau level) / (1 + exp( a*b - b*t)

...which provides a direct value for the peak rate at t = a without the need for differentiating the function.

Note 2) My data source was Worldometers.info - not a name that initially inspires confidence - which seems to provide a quite reliable data source for CV-19 data for this and other countries.
/end