Post #1206: COVID-19 trend, finishing up the week

Posted on August 7, 2021

The U.S. is now up to 33 new cases per 100K population per day.  The percentage growth in new cases continues to slow.

We won’t get another look at the trend until next Tuesday, as the majority of states don’t report numbers over the weekend.

Data source for this and other graphs of new case counts:  Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 8/7/2021, from https://github.com/nytimes/covid-19-data.”  The NY Times U.S. tracking page may be found at https://www.nytimes.com/interactive/2020/us/coronavirus-us-cases.html.

The percentage growth in new cases continues to fall (blue line below).

I’m of two minds about that.  It’s a good thing that this is showing “sub-exponential” growth.  In other words, that the percentage increase in new cases is falling from week to week.  On the other hand, hospital beds aren’t filled with percentages, they are filled with cases.  And the weekly increase in the number of daily new cases (the orange line) is continuing to grow at a steady pace.  Either way, if you keep that up long enough, the hospitals will be filled.  Exponential growth (1-2-4-8) will get us there faster, but arithmetic growth (1-2-3-4) will still get us there.

Louisiana and Florida continue to be the top two states, with 98 and 95 new cases / 100K / day, respectively.

I continue to imagine that the highest-volume states are starting to top out.  I keep thinking I see just a little downward curvature of the lines, for those states, compared to the rest.  (When graphed in logs.)  Like so:

If so, that’s pretty subtle.  When I sort the states by current new case volume, and aggregate by quintile (highest, next, middle, next, lowest), maybe there’s a little daylight between the line for the highest and a straight-line projection.  Or maybe that’s just a bit of statistical regression-to-the-mean, and means nothing.  Tough to say at this point.

The odds at 100 new cases / 100K / day.

I just thought it might be worth working through the crude odds of encountering an infectious individual, in those states where newly diagnosed cases are running at about 100 / 100K population / day.  You can take this and scale it down to the circumstances in your own state.

Factor in two weeks’ growth.  First, recall that there’s about two weeks between infection and full reporting in the data.  By contrast, if you are out and about today, you’ll be facing the currently-infectious population.  That population will have had about two weeks to grow in the meantime, compared to the reported case rates you are looking at today.

So the first fudge factor is your best guess as to two week’s growth in cases.  The current average rate of increase is just under 40% per week, and falling.  I’ll guess two consecutive weeks of 25% per week growth, for a total of (1.25 x 1.25 – 1 = ) 56% increase.

Factor in undiagnosed cases.  Even now, this remains guesswork.  If you rely on U.S. seroprevalence surveys, it looks like there’s only one un-diagnosed case for every diagnosed case.  Here’s the CDC data showing about 33.5M diagnosed cases as of mid-June 2021, versus about 70M people with some active antibodies showing prior infection with COVID-19.

Source:  CDC COVID data tracker.

I have gone through the issues with seroprevalence surveys in prior posts.  I expect that the true number of infections is substantially higher than just twice the diagnosed count.  (For one thing, a common estimate is that 40% of COVID-19 infections are asymptomatic.  Those individuals would rarely be tested).

I’m opting for a simple round-number estimate that there are three total infections for every one that is diagnosed.

Number of days infectious.  Finally, the 100 new cases / 100K / day is the people diagnosed on that date.  They’ve likely been capable of spreading infection for some days prior to that, for those who were symptomatic.  If they were mildly symptomatic or asymptomatic, they might be walking around for more than a week, capable of spreading COVID-19.  So you have to account for the average number of days for each each new day’s daily count of infected individuals wa infectious for.  I’m guessing an average of four days.

Source: “Variation in False-Negative Rate of Reverse Transcriptase Polymerase Chain Reaction–Based SARS-CoV-2 Tests by Time Since Exposure:, Kucirka, Lauren M, Lauer, Stephen A, Laeyendecker, Oliver, Boon, Denali, Lessler, Justin doi: 10.7326/M20-1495 Annals of Internal Medicine, May 13 2020, https://doi.org/10.7326/M20-1495

When I put that together, I get:

(100 / 100k) * 1.56 * 3 * 4 = 1872 infectious individuals / 100K population.

Or, in round numbers, 1.9% of the population.  Call it one person in 50.  In Florida or Louisiana today, arguably one person in 50 is capable of spreading COVID-19.

If you attend (say) a church service with 100 people, what are the odds that nobody in that church is currently infectious with COVID-19?  That’s (0.98 ^ 100 =) 13%.  In other words, there’s an 87% chance that in a room with 100 people, somebody in that room is capable of spreading COVID-19.

Here’s a kicker.  Say I’m off by a factor of two, in my calculation.  So it’s one person in 100, instead of one in 50.  Then what are the odds that the 100-person gathering has no COVID-19 infected individuals?  That’s .99 ^ 100, or about 37%.  You’d still have a 63% chance of sharing that space with a COVID-infected person.