Post #1119: COVID-19 trends, update to 4/22/2021.

Looks like the U.S. fourth wave is fizzling out.

You may have noticed that the news media are no longer screaming about Michigan.  That’s because things are getting somewhat better there, and that doesn’t make the news.

Source for this and all other graphs of new cases:  Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 4/23/2021.  The NY Times U.S. tracking page can be found at

More than that, the entire Midwest now seems to have topped at just about exactly the same time as Michigan. That’s the sort of synchronous behavior that makes me ask whether there’s still a large element of seasonality to this current wave of COVID-19.  Think about it.  Those states have widely-varying histories (fraction of population already infected), varying rates of vaccination, and varying policies toward (e.g.) re-opening of schools.  And yet, they all appear to peak within a few days of one another?  It’s tough for me to believe that there isn’t some underlying factor causing that behavior.

Be that as it may, more than four weeks into this fourth wave, the U.S. daily new case rate stands just 14% above the low point of the prior wave (marked in red below).  That works out to a growth rate of just 3 percent per week.  That’s not even remotely comparable to the prior three U.S. waves of COVID-19.

I keep using the term “fizzle out” to describe this U.S. fourth wave.  There are no new hotspots to take the place of Michigan.  On the other hand, the virus isn’t going away.  Not anywhere.  Or, at least, not in any state, not even those states that had a large fraction of the population immune via infection.

Here’s a graph of what was, at some time in the past, my top ten candidates for herd immunity, based on having a large share of the population immune via prior infection with COVID-19.   There’s absolutely nothing to suggest that any state is even close to herd immunity.

Tribe immunity

If I contrast what’s just been happening at William and Mary (Post #1117), versus what has happened in Michigan, I’m starting to see some depth to the herd immunity issue.

The W&M student body is largely isolated from the rest  of the world.  As of ten days ago, three-quarters of them had been vaccinated.  And they now appear to have very nearly eradicated COVID-19 within the student body, having had one positive case in the last 4500 or so tests, in the current round of “census” testing of every student on campus.

In Michigan, by contrast, the crisis arose because the virus found itself a fresh, largely uninfected population:  High school students.  The decision to re-open high schools created a pathway for spread of COVID-19 in a population that had largely been protected from it, or, at least, mostly uninfected by it, up to now.

W&M fits the classic model of herd immunity.  That’s a single, isolated, well-mixed population.  With a high vaccination rate, and almost uniformly good COVID-19 hygiene, they have all-but-eliminated the spread of COVID-19 on campus.

But in Michigan, we have numerous sub-groups of the population, and what we have seen of late is that the pandemic has remained alive by rotating to a new targeted group.  Fresh victims, as it were.  There, a large population of unvaccinated individuals  was newly exposed to a situation where transmission was likely.  And so the rapid spread of the virus continued.

Here’s the point:  Michigan wasn’t a flare-up of the virus in the entire population.  It’s not as if they saw a spike across-the-board.  It was mostly due to the spread of the virus to a new target group, high school students, and to a lesser degree, grade-school students and young adults.  My recollection is that for older adults, there wasn’t much of an increase at all in new cases per day.

Michigan had that sub-population of “fresh victims” standing by.  And Michigan saw that flare-up at a time when, according to the standard model of epidemics, infection rates should be tapering off.  Michigan seems to defy the rules, but that’s because the rules don’t really fit the situation in Michigan.

By contrast, within the W&M student body, there is no group of fresh victims for the virus to turn to.  That’s a more-or-less a homogeneous mass of people, living in its own little world.  The refer themselves as the Tribe, and that’s oddly appropriate in this context.  They are a most-vaccinated tribe, and the results are following the standard theory of epidemics.  Tribe immunity, if you will.

Prostatectomies per 100,000 men;  COVID-19 cases per 100,000 non-immune individuals.

In the field of public health, some disease rates are not calculated on a per-person basis.  For example, you won’t see figures for prostatectomies per 100,000 persons.  You will see figures for prostactomies per 100,000 men.  That’s for the obvious reason that women are irrelevant to that calculation, and it makes more sense to calculate incidence of surgery per 100,000 potentially eligible for that surgery.  (You might not think that matters, but if you stratify by age, you’ll find that men account for just 40% of the population age 75+).

A recent Washington Post opinion piece offered a truly profound insight into the current situation with COVID-19.  (Opinion: This is the most dangerous moment to be unvaccinated, by Robert M. Wachter, April 19, 2021).  Or, at least, I found it to be truly profound.  Let me summarize the gist of it, with a little twist.

If you start counting up all the people who are now immune to COVID-19, you realize that the rate of new infections among those who are still capable of being infected is really pretty horrendous.  

The current U.S. new-infection rate doesn’t look too bad, but that’s because we calculate it as new infections divided by the total population. When we do that, we get an average of about 20 new cases / 100,000 population / day.

But when you think about it, that’s like prostatectomies per capita, not per male.  It’s not really an accurate picture of what’s going on.  A large fraction of the population is now immune to  COVID-19, starting with more than half of the adult population having been vaccinated. 

Let me bring my “herd immunity” chart up to date, and then discuss that point.

Source:  Calculated, with a separate assumption as to the ratio of total infections to reported infections, based on the CDC COVID Data Tracker as of 4/22/2021.

By my best-guess estimate, more than two-thirds of the U.S. population should be fully immune to COVID-19 at this point.  And so, when you see the U.S. new-case rate of 20/100K/day,  based on the total population, you should mentally triple that, and say, that’s 60 new cases /100,000 population /day within the population that’s still at risk for infection.

Once you get that in perspective, you see the current situation in a new light.  The U.K. variant is raging within the population still at risk.  The only reason we don’t see that is that two-thirds of the population is no longer at risk.  And when we average those two populations together — 60/100K/day and 0/100K/day — we end up with the seemingly-OK published value of 20/100K/day.

That gets back to the fundamental question for the end of the pandemic:  If two-thirds of us are immune, and we continue to engage in COVID-19 hygiene, why is there still no sign of herd immunity?  That immunity by itself should be able to handle a virus with a basic replication factor (R-nought) of 3.  Toss in the COVID-19 hygiene, and that plausibly should handle the U.K. variant, with an estimated R-nought of maybe 3.5.  Why isn’t that happening yet?

I think the explanation is that the new, more infectious U.K. variant is now finding fresh victims.  It’s jumping to people who would not have been infected, in their normal course of business with the older, less-infectious variant.  As a result, cases are skyrocketing among the portion of the population that remains at risk for infection.

So the U.S. as a whole, with the new U.K. variant being spread, perhaps does not fit the standard model of a pandemic.  It’s not like William and Mary, with a homogenous and well-mixed population.  It’s more like Michigan, with pockets of fresh victims ready to be infected, if only some pathway opens up for the virus to reach them.  And, plausibly, the greater infectiousness of the U.K. variant is the pathway by which the virus continues to spread within the remaining small, non-immune population.

In conclusion:  I haven’t quite figured out what this means for the end of the pandemic.  But, at least, I think this explains why we’re not seeing a swift and clean end of the pandemic, as seems to be occurring at William and Mary.  All across the country, the introduction of the more-infectious U.K. variant means that we’re finding the equivalent of Michigan’s high school students.  We’re finding fresh victims who would not otherwise have become infected.  And we’re now going to have to wait for that process to work itself out before we finally get the total level of immunity in the population both high enough, and homogeneous enough, to suppress further transmission of the virus.

Post #1117: William and Mary, another good day, the math of herd immunity.

Today’s test results were 1-for-1772.  Three days of census testing are highlighted in yellow below.  In short, they’ve tested three-quarters of campus enrollment and found one COVID-19 case.

Again, obviously good news.

This is a follow-up to my last post, and in this I try to explain why you might not want to, or be able to, relax the William and Mary COVID-19 hygiene rules just yet.  Despite this good news. Continue reading Post #1117: William and Mary, another good day, the math of herd immunity.

Post #1115: William and Mary, zero cases in a further 1599 tests? Sure looks like herd immunity.

Edit:  Oh, no.  My wife tells me this is prompting calls to ease up on the COVID-19 hygiene at William and Mary.    I know it’s tough to grasp, but that arithmetic of epidemics says that would be unwise. 

It’s too late this evening, but I’ll write up the math on that one tomorrow.  Until the virus is no longer in circulation anywhere, the way you keep it from entering and spreading in the W&M student body is via the combination of vaccination and COVID-19 hygiene.  I realize that “herd immunity” is rarely discussed this way, but it’s the combination of those two effects that reduces the transmission rate enough to get you over the herd immunity threshold. 

You risk firing this right back up again if you drop the COVID-19 hygiene portion of this system, given the incidence of new cases in the community.

Original post follows:

Yesterday W&M reported zero new cases in 1488 tests.  Today they reported zero new cases in a further 1599 tests.

Like so:

It’s extremely unlikely that we would observe this, if the recent rate of new infections was continuing.  That’s what yesterday’s math showed. Continue reading Post #1115: William and Mary, zero cases in a further 1599 tests? Sure looks like herd immunity.

Post #1113: William and Mary, zero cases in 1400+ tests. Herd immunity?

William and Mary has started another round of “census” testing, administering COVID-19 tests to all students on the campus.  Yesterday, an email from the W&M administration said that test results should start appearing on the W&M COVID-19 dashboard.  And they have.

Yesterday, W&M reported test results for 1448 students.  They found no (zero) positives.  Zero new COVID-19 cases, out of 1448 tested. Continue reading Post #1113: William and Mary, zero cases in 1400+ tests. Herd immunity?

Post #1112: COVID-19 trends to 4/18/2021

Is this the peak of the U.S. fourth wave?

Below is the U.S. and regional graph, in logs.  There really hasn’t been a trend to speak of for more than two weeks now.  But now, most of those regional graphs are starting to bend downward.

This past few days, all the places that were hotspots seemed to be getting a break.  The thing that started to look like a peak, for Michigan, a few days back, looks like even more of a peak now.  Minnesota seems to have gotten to a plateau.  All the other places where the U.K. variant is known to be highly prevalent are doing, well, pretty much nothing.  Like so:

Even Colorado, which was the outlier among Mountain states, and the Mountain state with the highest incidence of the U.K. variant, got little break:

The situation isn’t uniformly rosy.  Maine, which had largely been bypassed by COVID-19 in the earlier waves, now has a strong upward trend in new cases per day.  Both Oregon and Washington still have upward trends (but fairly low absolute rates of new cases per day).  Otherwise, you really have to look hard to find any dark clouds on the horizon.

Separately, vaccinations continue apace.  As I noted some time ago, these daily vaccination numbers have some issues.  In particular, they have a strong regular weekly cycle, so if you catch Sunday between your snapshots, it’ll look like the pace of vaccination has slowed.  (Which this next pair of snapshots does.)

I keep hearing news coverage about vaccination rates slowing down, and vaccine “hesitancy” and blah blah blah.  Sure as heck isn’t showing up in the national data.  I wonder of that’s a case of the news media cherry-picking a few places that make a good story.  But overlooking the actual U.S. trend.

Over the past three days, the elderly added another 0.33 percentage points per day, and the U.S. averaged about 3.7M vaccine shots per day.

Today’s data glitch:  I guess it had to happen sometime.  Month after month, states would find old cases and add then dump those into their case counts, generating a “speed bump” in their data.  On 4/17/2021, Missouri found over 7,000 old duplicate cases, and removed them from their case counts, per this documentation, creating, I guess, a “speed dip” in their data?  The problem is that  you can’t plot negative numbers on a log scale.  So I’m tossing those 7500 or so cases back into the Missouri data, and getting on with it.

Post #1110: William and Mary, no COVID-19 uptick following spring break days

William and Mary had a COVID-19 outbreak following St. Patrick’s day.  There was some concern that we might see another such outbreak following two back-to-back spring break days last week (April 6th and 7th).  In my last post (Post #1099), I said I’d check in again to see whether there was an uptick following spring break.  Continue reading Post #1110: William and Mary, no COVID-19 uptick following spring break days

Post #1107: COVID-19 trend to 4-13-2021

Not much to say, really.  No material change from prior trends.  US trend is slightly up.  Michigan is almost up to 80 new cases / 100,000 / day, so they’re right where they were at the peak of the U.S. third wave.  The five states with the highest proportion of the U.K. variant are moving in five different directions.  And the elderly continue to get vaccinated, defying all prior survey-based estimates.

U.S. trend remains slightly up.

Michigan has almost reached 80 new cases/ 100,000 per day.  So they’re back into U.S. third wave territory.  But Minnesota isn’t anywhere near its U.S. third wave peak.  And I’ve made the argument that this is cause-and-effect.  Part of Michigan’s problem is that it has a low proportion of the population immune to COVID-19 due to generally low rates of infection in the earlier waves.

The dates are unreadable, but this one spans 10/1/2020 to the present, to show the U.S. third wave.

But it’s not as if all the states with high incidence of the U.K. variant are following Michigan’s path.  Michigan remains an outlier.


The elderly continue to get vaccinated.  Last three days, that rate was a bit under 0.4 percentage points per day.  Almost sure to break 80% in the next day or two.  Far more than was suggested by survey data.



Post #1106: COVID-19 trend to 4/11/2021


Opinions vary on what’s going to happen next in the U.S. fourth wave of COVID-19.  At one end of the spectrum, there’s the CDC director, talking up “impending doom” from the U.S. fourth wave.  And you’ll see sporadic newspaper stories where some expert will opine that a massive U.S. fourth wave of COVID-19 is approaching.  Or might be approaching.  Or at least remains enough of a likelihood that you should keep up your COVID-19 hygiene and get yourself vaccinated.

My post today is a reaction to a news article proclaiming that we’re all going to go the way of Michigan.  With, as far as I can tell, zero hard analysis to back that up.  Certainly, nothing like a statistical analysis of the state-level data (Post #1101), or a detailed outline of the factors that make Michigan particularly vulnerable (Post #1105).

Near as I can tell, that’s straight-up fear-based journalism.  The article more-or-less blames the people of Michigan for being a bunch of COVID-19 hygiene slackers.  When, in fact, that’s just not objectively true.   Or, at least, they’re no worse than 35 or so other states. Continue reading Post #1106: COVID-19 trend to 4/11/2021

Post #1104: Sidewalks, one last try at clarifying the issue.

I’m just going to make a few simple points here that may have been missed in my last post.  I made the mistake of thinking that everybody knew this.  That’s my error, and I’ll try to correct it now.

These point are that:

  1. The Town of Vienna strenuously objected to the narrow interpretation of the Robinson bequest.  They didn’t agree with it.
  2. A lawsuit in this case is the professional way to have differences in interpretation of a legal document resolved through the legal system by a disinterested, trained legal expert (the judge).
  3. My opinion of what the intent of the document was does not matter.
  4. The legal impediment to using the money is what matters.  Unless you change that, the Town of Vienna’s current plans are as good as it gets.

Continue reading Post #1104: Sidewalks, one last try at clarifying the issue.