Post #1259: COVID-19 trend, ending the week

The U.S. as a whole is now 10% below the 9/1/2021 peak of the Delta wave.  We stand at 46.1 new cases / 100K / day, down from 46.6 yesterday.

A month ago, when I first tried to predict the peak of the Delta wave, and came up with “early September”, an astute reader suggested that the wave for the U.S. as a whole ought to be much “broader” than the waves for the individual states.  In hindsight, I’m going to say,  that seems to be correct.

Overall, for the past week, the number of new cases is essentially unchanged.  But that’s due to that big “divot” in the curve, depressing the case counts last week.  I’ve found no clear explanation for that “divot”.  At this point, I’m going to attribute it to an inexplicably large impact of the Labor Day holiday on testing and reporting of testing.  In the past, major national holidays produced impact of that size.  We’d just never seen anything like that before for (e.g.) Memorial Day, July 4th, or Labor Day.

If I airbrush that out, and bridge the gap, I get a plausible, if somewhat broad, shape to the peak.

In short, despite all my panicky posts of the past week, it appears that the U.S. merely continues to grind through the Delta wave.  Which, as of now, peaked on 9/1/2021.

As with prior waves, we’re seeing groups of state move into the U.S. peak position and then have their new case counts decline.

Florida, for example, has now fallen more than 50% since its 8/28/2021 peak of 112 new cases /  100K/ day, on the last day of August.  They are currently (9/17/2021 data) at 54.

The initial group of states that led the wave — FL, LA, MA — are all on the down-side of it.  We’ve had an intermediate group show up.  And now the three states with more than 100 new COVID-19 cases / 100K / day are SC, TN, WV.  It’s pretty clear that Alaska is on track to hit that.

The pandemic continues to show considerable geographic clustering.  If I separate out the states that had high rates, but appear to have peaked, I get the Gulf states, less Texas, pus Georgia:

Beyond that, it’s difficult to generalize about the next set of states — the states with high and rising case rates.  It looks like the southern Appalachians are represented, as is Alaska.  Not visible, Montana would also make the cut based on the current high rate of growth there.

So that’s how it looks today. The Gulf states (ex TX) seem to have peaked.  Fl, LA, MS are now at about half the rate of daily new cases that they were three weeks ago.  A couple of neighboring states (GA, AL) seemed to have peaked maybe a week later.

Now we just have to wait for this to work through the rest of the states.  And then, at some point, it will probably converge with a winter wave.

Updating the herd immunity table

I should update my “herd immunity” table.  This is my best guess at to the fraction of each state’s population that is immune to COVID-19.

This never did have much accuracy, owing to the need to make a couple of fairly critical (but nearly data-free) assumptions.  As time passes, it gets even less accurate, for two key reasons.

First, immunity fades.  That’s true of natural immunity (following infection) or immunity acquired via vaccine.  As the pandemic stretches on, it becomes increasingly dubious to count people who were infected a year ago, or vaccinated 7 months ago, as immune to COVID-19.

Second, widespread home testing with antigen (quick) tests likely reduces the fraction of the population of truly infected individuals that are formally diagnosed with COVID-19 and counted in the state data.  (Restated, increases the ratio of actual, total cases to diagnosed cases counted by state health departments.)

Those antigen tests don’t need to be sent to a lab, so they are not reported to state health departments.  And, near as I can tell, they appear to have a low false-positive rate.  All of that means that if you give yourself an antigen test, you don’t really need to do anything else, testing-wise.  Unless you did something to trigger a false positive (such as drinking an acidic beverage before testing), you can be fairly sure that you’ve got COVID-19 if you get a positive reading.  (By contrast, they have a fairly high false negative rate, so if you get a negative reading, there’s still a good chance that you do have COVID).

I think the magnitudes of both of those effects are unknown.  And I’m ignoring them for now.

So, FWIW, here are my “standard” assumptions, and the results I get (data is as of about a week ago).

  • Two un-diagnosed cases for every formally diagnosed-and-counted case.
  • Full vaccination is 84% effective against Delta, on average.
  • Partial vaccination is 54% effective against Delta.
  • Immunity from prior infection is 84% effective against Delta.
  • People get vaccinations at random, regardless of whether they have had a prior infection.  (I need this last one to net out the assumed overlap of the prior-infection and vaccination populations).

The table shows the estimated fraction of the population that is totally immune.  E.g., if there were 100 people fully vaccinated, I’d count 84 as being totally immune, based on the assumed 84% effectiveness of the vaccines.

Source:  Calculated from data on the CDC COVID data tracker, using the assumptions listed above.

I should point out a few things.

First, the high-immunity states are a motley crew.  It’s a mix of high-vaccination states, and high-cumulative-infection-rate states.

Second, the high-immunity states are not very well correlated with who is doing well and poorly right now.  In part, that’s because you might start to reach high immunity during the Delta wave.  In other words, if infection is rampant in your state now (as in Tennessee), that’s pushing you up this list.

Third, in this calculation, 80% is the magic number.  (Not 90+%, because I’ve already adjusted for the effectiveness of the vaccines.)  If the “R-nought” of the Delta variant is 5.0 (which seems to be somewhere around the consensus), then you need to have 80% fully immune to reach herd immunity (in the sense that the pandemic would die off even if you took no other precautions such as wearing masks, limiting social interaction, and so on.)

(Explanation:  If each infected person would infect five others absent an intervention, you need to block at least four of those new infections to get the pool of infected individuals to shrink.  Hence, R-nought of 5.0 requires 80% full immunity to achieve herd immunity.)

I’m just pointing out that, with all the shortcomings and assumptions and so on, this is the first time that any state has every reached what would be, in theory, the herd immunity number.  (Using my current (more refined) set of assumptions).

This is, in part, why my guess remains that we’re going to have a fairly bad winter wave this year, and then we’ll be done with this.  COVID-19 will always be lurking in the background, but it won’t be epidemic in the U.S.

Why? Project this table forward, using last year’s winter wave.  The U.S. had about 20 million diagnosed cases in last year’s winter wave.  That’s an estimated 60 million actual cases, under my assumptions, or about 18% of the U.S. population.  Start tacking 18%s to the numbers above, and everybody from Virginia on up would have hit the magic 80%.

In round numbers, best guess, one more awful winter wave should put the majority of the country at or near the herd immunity level for Delta.  Add in a few other factors that also interrupt infections (masking, limits on social activity) and we should at least be in the ballpark.  I hope.

Post #1258: William and Mary, wrapping up, total of 36 new cases for the week.

I’ve been asked to keep posting my tabulation of new COVID-19 cases at William and Mary.  Let me do this once a week, on Friday, assuming there’s nothing newsworthy going on.  You can’t recover the daily information directly from the  William and Mary COVID-19 dashboard.

That 36 cases is better than last week, but it’s still a bit high compared to college-age Virginians as a whole.  Using VA Department of Health data for those age 18-24, for this past week, at the all-Virginia age 18-24 new case rate,  we’d have expected 22 cases this week, for the roughly 6600 students on campus.  That does not account for differences in vaccination rate, testing rate, and so on between the William and Mary student body and the Virginia college-age population.  All it shows is that we’re somewhere in the ballpark of normal for a Virginia college-age population.


Post #1255: COVID-19 trend to 9/15/2021

New COVID-19 cases are up 3% over the past seven days.  But we’re still 4% below the 9/1/2021 peak of the Delta wave.  Currently, we’re at 47.3 new cases / 100K / day, down from a revised 47.9 cases yesterday.   The overwhelming majority of states showed an increase in new COVID-19 cases over the past seven days.

Here’s my regional graph in logs and natural units.


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 9/16/2021, from”  The NY Times U.S. tracking page may be found at

In the log graph, it appears that the nice orderly structure of the Delta wave is starting to break down.  For the past month, the regional trends formed a set of (near) parallel lines.  That is, the regions had similar rates of growth in new COVID-19 cases.  That’s starting to get lost as you get to the right side of the chart.

If we compare the first and second years of the U.S. pandemic (below, graph starts April 1 of each year), this last little episode just looks like a post-holiday blip.  E.g., the wiggles in last year’s winter wave (tallest part of the blue line)  were due to Thanksgiving and Christmas/New Year holidays, respectively.

That problem with that hypothesis is that Labor Day is nowhere near as big a holiday as Thanksgiving.  Which is what appears to be case on the chart above — the “hook” on the end of the red line is about as deep as the first wiggle on last year’s winter wave.  On the other hand, data reporting was more continuous last year.  States weren’t taking the weekends off, as is now commonly the case.  Maybe a minor holiday, combined with sporadic data reporting, can produce that much of a disruption in the numbers now.

But the bottom line is that I can’t find any solid evidence, so far, that this latest change is being driven by anything in particular.

There is no systematic data source that lets me look at cases by age in a timely fashion, so the idea that this latest change is due to schools can’t be tested.

And as for the onset of the winter wave, it’s just too soon to tell.  Growth in daily new COVID-19 cases has definitely shifted into the northern half of the country, as you can see below:

Map courtesy of

That's a lot clearer if I simplify the map to just three colors, below.  Now, with the exception of Louisiana and Illinois, the separation of the states is quite stark.

Map courtesy of

The upshot is that I've gone from having a pretty solid prediction for the last month, to being totally lost as of today.

One option is that this is just a post-holiday disruption of testing and reporting, as we saw happen last year.  But it's grossly disproportionate to the size of the holiday, compared to last year.  And the regional lines are starting to get disorderly, which is what has happened in the past at an inflection point in the curve.

A second option is that this is due to school re-opening.  But there's no hard data yet, on a national level.  All I can get is newspaper reporting, and the occasional state where cases are reported by age.  In Virginia, where I can get the data, there appears to be no upsurge in cases for school-aged children.

Yet a third option is that this is the start of the winter wave.  New-case growth has shifted to the northern half of the country, as it did for last year's winter wave.  But it's at least a month too soon for that to start happening, compared to last year.  On the other hand, Delta is substantially easier to spread than the native variant that was prevalent last year.  So maybe that shifts the timing.

We'll just have to wait and see.

Post #1254: Update for William and Mary: That’s good.

The William and Mary COVID-19 dashboard doesn’t track day-to-day changes.  That’s why I’ve been writing down each day’s numbers, as shown above.

Last night’s update showed three new cases.    That’s unremarkable.  It’s just about the rate you’d expect for an average college-age population in Virginia.

Given that, I’m not going to post about this for a while, unless there’s some material uptick in the new case numbers.

Good news is no news, or something like that.

Post #1253: COVID-19 trend to 9/14/2021, not according to plan.


The Labor Day holiday scrambled the data on new U.S. COVID-19 cases.  Today, that should all have been sorted out, and we should get a clear look at the trend.

Unfortunately, the trend looks ugly.  Today the U.S. stands at 47.3 new COVID-19 cases / 100K / day, up two from two days ago. The case count is right where it was one week ago. Continue reading Post #1253: COVID-19 trend to 9/14/2021, not according to plan.

Post #1252: COVID situation at William and Mary appears to settle down


Last night’s update of the William and Mary COVID-19 dashboard showed just over 46 new positives for the prior three days.

Last year, when William and Mary itself was doing all the testing, it was hard to interpret the Monday count.  The numbers had a strong up-and-down pattern over the course of the week, presumably reflecting W&Ms schedule for routine testing.

But now, by contrast, most (possibly all) of what we are seeing is testing for cause.  The new COVID cases above are a mix of individuals who had themselves tested ( and reported a positive test to W&M), and symptomatic or known exposed individuals who are being tested by W&M and found to be positive.

(At some point, there will also be ongoing screening testing of the unvaccinated.  And, later in the semester, W&M will test a random sample of students to estimate the prevalence of COVID-19 on campus.  But for now, I think it’s mostly diagnostic testing, that is, testing for cause).

Based on that, my guess is that the test results are coming in a fairly steady stream right now.

If that’s true, we can tentatively say that the low number of new positives, per day, for the past three days, is an indication that the true rate of new positive cases per day has backed down from last week’s peak.

Obviously, there’s not enough information there to declare victory.  But, arguably, there’s enough to declare non-disaster.  As of today, it doesn’t look like this is any sort of out-of-hand rapidly-escalating mess.  


Post #1251: COVID-19 trend to 9/13/2021, I can’t fix the data today

Whatever U.S. COVID-19 case count you see today is either going to be grossly wrong or partly fictional.  Maybe both.  Mine included.

My best guess is that the U.S. Delta wave continued to recede slowly over the weekend.  But that is just a guess.  We won’t really have any hard data on that until tomorrow at the earliest.

This post explains the problem with today’s data.  It’s clear that the raw data aren’t usable, and I can’t quite seem to come up with a fix.

Continue reading Post #1251: COVID-19 trend to 9/13/2021, I can’t fix the data today

Post #1249: A first-hand lesson on why we still have a pandemic

Source:  Wikipedia

Yesterday, my wife and I got onto a bus packed with un-masked strangers.   When we got to where we were going, we spent some time in indoor spaces packed with loud crowds of eating, drinking, non-masked-wearing strangers.  Then we got back on that bus and went home.

In hindsight, this may not have been the smartest thing we ever did.  It takes just a little math to realize it’s a pretty good bet that some COVID was spread at the event we attended.

It wasn’t our intention to do that.  It never is, I guess.  All I really wanted was a nice plate of pirohi.  What I got was a lesson in why we’re still in a pandemic.  Or, at least, in how thoughtless the average American is.

Continue reading Post #1249: A first-hand lesson on why we still have a pandemic