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
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