The Growth Rate of US Coronavirus Cases Has Decreased

The Growth Rate of US Coronavirus Cases Has Decreased

Many sources have tracked the Johns Hopkins University Coronavirus cases and presented either extreme growth or exponential growth comparisons.   I have forgotten all of my graphics methods, but I have been calculating the fluctuating growth rates daily for a month.  An exponential growth is really multiply by a fixed factor every day, of (1+r), where r is the growth rate.  Yes, this is the same as compound interest, with interest rate r.

The Coronavirus data is as far from a controlled scientific experiment as you can get.   Experiments involve accurate measurements, and clear definitions of what you are measuring, and what equipment you are using to make the experiment reproducible (perish the thought).  We have never had enough testing to test more than the fifth of those with Coronavirus who need hospitalization.  Since positive tests are now running 5% to 35%, we were mistaking colds and flu viruses for similar symptoms.  The Chinese even went from Coronavirus testing to clinical evaluation, and got a large jump.  The nature of US tests have been constantly changing.  There has always been about a week delay in the tests.  The occurrence of symptoms is not immediate, averaging about 5 days, but extending to the adopted 14 day quarantine time.  Some remained asymptomatic, or showed only mild symptoms.  Even now, the results of all tests are not being reported to the federal government.  The criteria of who would be tested has varied between locations, and over time.  Tests are still being doled out by the government.

Then there is the response with mitigation, which has varied across the country, and with different starting times, and strictness of mitigations.   The rules have also gotten stricter over time.   So even if you had a theory of a function that should be the growth function, it couldn’t possibly be tested here.

In the US, the only thing really being tested belongs in theories of chaos, run by a politically dominated narcissist as a psychological theory, and a theory of denialism and misinformation.

We know the standard exponential growth curves, and I have seen recent UCI work with exponential followed by power law growth, and the emperical error function used by the IHME University of Washington prediction model partly used by the White House Coronavirus Task Force.   In my simple and simplistic approach, we just look at the daily percent increases, and notice the change, without a model.

Here is a table of the dates and the growth rate each day as a percent.  We also note which days are Mondays, to see if there is a weekend effect of measuring or reporting.

Date Daily Percent Increase
4/3 Friday 12.2
13.3
4/1 14.3
3/31 15.4
3/30 Monday 15.3
14.5
19.7
21.4
24.1
25.4
17.0
3/23 Monday 41.4
25.2
35.4
27.4
51.4
48.2
37.0
3/16 Monday 23.9
28.5
36.9
32.0
28.2
29.9
39.4
3/9 Monday 24.2
33.0
34.9
44.7
64.9
42.5
3/3 Tuesday 33.3

Leaving out the high and the low for a week, the first week ranged from 33% to 45% growth, starting on Tuesday, 3/3.

The second week ranged from 29% to 37%, leaving out the highest and lowest values, as we will do for each week.

The third week ranged from 27% to 48%.

The fourth week ranged from 15% to 24%.

The last four days ranged from 12% to 15%, leaving none out.

Clearly, the ranges of the last two weeks, as treated above, don’t even overlap with the much higher rates of the first three weeks.

This shows a great positive success of the even partial social distancing, since that term and concept was invented.

If we take 14% as the future rate of increase, or 1.14 as the daily multiplicative factor, it doubles in a week.  We are, of course, hoping for a turnover in ten days.

About Dennis SILVERMAN

I am a retired Professor of Physics and Astronomy at U C Irvine. For a decade I have been active in learning about energy and the environment, and in lecturing and attending classes at the Osher Lifelong Learning Institute (OLLI) at UC Irvine.
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