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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
Web Result with Site Links
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