Post #1145: COVID-19, finally seeing the herd immunity graph


Yesterday I used the most recently-released CDC seroprevalence data to correct my national and state-level “herd immunity” estimates.  I reduced my estimate for the number of COVID-19 infections that were never formally diagnosed with a positive PCR or antigen test.

The resulting table provides a plausible estimate of the fraction of each state’s  population that is immune to COVID-19.  It combines vaccinations (a known number) and prior COVID-19 infections (an estimate), and makes a reasonable  attempt to take out the overlap between the two.  The end result is an estimate of where each state stands on the path to herd immunity.

Now I should do the obvious thing:  Plot that state-level estimate of population immunity against the recent trend in new cases, by state.  If we’re approaching herd immunity, a higher the level of immunity in the population should be correlated with a more rapid retreat of the pandemic.

Base on that logic, does it look like we’re achieving herd immunity?  My answer is yes, it sure looks like it to me. Continue reading Post #1145: COVID-19, finally seeing the herd immunity graph

Post #1144: COVID-19 seroprevalence surveys and re-thinking my estimate of herd immunity

Source:  Calculated from CDC state-level COVID-19 seroprevalence data from early March 2021, and counts of persons who tested positive for COVID-19, at various times, from the New York Times COVID-19 data repository.  Both sources accessed 5/12/2021.

I’ve been re-examining the CDC’s most recent seroprevalence survey results.  This post is the result of that.

A seroprevalence survey looks for antibodies to COVID-19 in blood samples.  It gives you an estimate of the number of people who were ever infected with COVID-19 at some point in the past.  Combing that with past and current counts of persons with a positive COVID-19 test, you can estimate the current number of people who should be immune to COVID-19 due to prior infection.  That number, along with the number of vaccinated individuals, feeds into any estimate of how close the population is to achieving “herd immunity”.

Based on the most recent CDC seroprevalence survey, the bad news is that we’re probably not as close to herd immunity as I thought we were. I was basing my herd immunity estimate on older data — the tall bars at the left side of the graph above.  In the past, there appeared to be more than four total infections for every positive test.  But now, that ratio is much closer to two infections for every positive test.  This means that I overstated the true fraction of the population that is immune to COVID-19 due to a prior infection.

The good news is, protective antibodies from prior COVID-19 infection appear to last a long time.  The simple statistical analysis above shows that people who were infected with COVID-19 more than nine months ago still appear to have enough circulating antibodies to be picked up as positives in a seroprevalence study.

Details follow.

Background:  Seroprevalence studies of COVID-19.

Three types of tests.  First, if you don’t know about the three different types of COVID-19 tests, this reference is one of many good plain-English explanations.   Briefly:

  • A DNA or PCR test looks for a current infection by checking for fragments of the DNA of the COVID-19 virus.  This is the original COVID-19 test.
  • An antigen or “rapid” test looks for a current infection by checking for proteins found on the surface of the virus.  This test came along some months after the pandemic hit.
  • A blood or serology test looks for any past infection by checking for any of several types of antibodies to COVID-19 in the blood.

When you see counts of COVID-19 cases, in most states, you are looking at counts of persons who tested positive with either a PCR test or an antigen test.  At the start of the pandemic, only the PCR tests were counted.  But as the antigen tests became more common, almost all states switched to counting either a PCR test or an antigen test as an actively infected individual.

See Post #1016 for a full write up of this change in case count reporting, and the large fraction of “probable” cases that now enter the count because they have a positive antigen test.


Significant under-count of actual infections from PCR and antigen tests.  It is well known that the count of positive COVID-19 tests (PCR plus antigen) grossly understates the true number of COVID-19 infections.  This was evident from the first analysis of the original Wuhan epidemic, where a large number of cases never received a formal positive diagnosis.  The same has held true for virtually every location where that issue has been examined.    For example, here’s a CDC estimate of a roughly fifteen-fold under-count of true COVID-19 cases in the pediatric population of Mississippi.

The under-counting occurs for several reasons.

  • Some people have no symptoms and so have no reason to get tested.  Dr. Fauci estimated that asymptomatic cases account for about 40% of all U.S. cases).  This will be even more true of the pediatric (under-age-18) population, where asymptomatic cases are more common than they are among adults.)
  • Others have symptoms but, for some reason, did not get tested.  That might have been due to a shortage of tests early in the pandemic, or to unwillingness to be tested.  There is no good estimate of that factor.
  • Yet a third factor leading to understatement of the true number of infections is the high false-negative rate of the DNA (PCR) COVID test (Post #859).  A single PCR test has somewhere around a 25% chance of missing a true COVID-19 infection.
  • And a fourth factor is the even higher false-negative rate of antigen tests.  These cheaper, faster tests look for specific proteins on the surface of the COVID-19, and the chance that a single antigen test will miss an active COVID-19 infection is around 50%.

Blood tests for antibodies are not perfect. I went through the ins and outs of blood testing for COVID-19 antibodies in Post #940.  There are several ways in which blood tests — and in particular the CDC’s seroprevalence surveys — can understate the true count of past COVID-19 infections.  That is, these tests also have a non-neglible false-negative rate.

  • Persons with asymptomatic or mild cases may have too few circulating antibodies to trigger a positive on the blood antibody test.
  • In particular, the most commonly-used antibody tests are not sensitive to those mild cases (per this review of the evidence on seroprevalence testing for COVID-19).
  • Antibody levels may decline over time, so that persons with infections early in the pandemic may still retain some immunity, but fail to trigger a positive on a blood test.
  • More recently, there is the potential to confound the results of immunization with the results of infection, but this is a matter of selecting which antibody types to test for.  (This is evident from the CDC web page cited above).

Even in populations where not much time has elapsed since infection, high-quality antibody blood testing still has a significant false negative rate.  In this study of Spanish health-care workers, around 10% of persons known to have been infected with COVID-19 were missed by a comprehensive set of blood antibody tests.

Finally, the sample of persons used for the actual CDC prevalence surveys is a sample of convenience.  They just re-use blood drawn for routine testing, such as (e.g.) cholesterol tests or screening “panels” (multichannel automated tests).   And the CDC only relies on two national laboratory companies.  The extent to which the CDC’s sample differs from the U.S. population as a whole is unknown.

The evolving relationship between the count of positive COVID-19 tests and estimates of seroprevalence.

I looked at the available CDC COVID-19 seroprevalence survey data back in early January (Post #933).  At that time, they had two rounds of survey data.  In the earliest round (circa August 1, 2020), by my calculation they found about five total infections for every one that had been reported via a PCR COVID-19 test.  In their second round (circa September 15, 2020), by my calculation, they found about four total infections for every one that had been reported via PRC test.

I didn’t make much of it at the time, because the methods clearly were pretty crude.  For example, their method didn’t seem to give reliable methods at the state level.  Two points does not make a trend under those circumstances.

I then looked at what evidence was available, including the likely fraction of cases missed by seroprevalence tests, the correlation of the seroprevalence and test count data across states, and so on.  I decided at that time to use a nice, round, five-to-one ratio for estimating total COVID-19 infections.  That is, for every positive COVID-19 test, I would assume that four more individuals had been infected but did not receive a positive COVID-19 test.  That’s all laid out in Post #940.

As you can see from the graph I did back in January, the linear trend line (in a cross-section of states) from the (then) last round of data shows about 3.7 total infections for every diagnosed infection.  That was just slightly lower than the ratio I got by simply adding up all the state-level seroprevalence estimates, weighting by state population.

Four things have changed since then.

First, the CDC has expanded that seroprevalence survey, and produces new estimates by state, every two weeks.  The most recent set of estimates date to early March.

Second, the mix of tests has changes.   In general, tests have become much more readily available, and, with “spit” tests, less intrusive.  (No more swab-up-the-nose.)  Currently, about a third of positive COVID-19 tests reported in the country are the antigen “rapid tests”, not the PCR tests.

This would argue for seeing a true lower ratio of total infections to total positive tests.   The easier it is to obtain a test, the more likely symptomatic individuals are to get tested.

Third, the age mix of the pandemic has shifted toward much younger people.  In some states, such as Michigan, the highest-incidence age group is high school students.  But this population has more asymptomatic infections.

It’s not clear what this would do to the ratio of total infections to total positive tests.  Asymptomatic individuals tend not to get tested, but they also tend to be missed by the blood antibody tests.  In effect, some portion of true infections will be skipped in both the numerator and denominator of the ratio of total infections to total positive PCR/antigen tests.

Four, a lot of time has passed.  As immunity or antibody levels fade over time, presumably the ratio of total persons found via blood antibody test, to persons ever found via PCR/antibody test, will fall.

That said, there’s no harm in re-doing the graph above, using the most recent CDC seroprevalence data, and counts of known infections based on PCR/antigen tests.

But now, the correlation across states suggests just 2.2 total COVID-19 infections for every person diagnosed with PCR/antigen testing.  As before, the direction calculation from the data, weighting the state estimates by state population, yields a slightly higher estimate.  In this case, the direct calculation yields about 2.3 total infections for every positive PCR/antigen test.

The first question to answer is whether or not this is due to immunity or antibody levels fading over time.   To answer that, I did a little “regression analysis”.  I broke up the population with positive PCR/antigen test into cohorts depending on how long ago they tested positive.  (More than 9 months ago, 6 to 9 months ago, 3 to 6 months ago, under 3 months ago, all starting from March 12, 2021, which is the mid-point of the latest seroprevalence test data).  Then I tried to predict the state-level seroprevalence based on the fraction of each state’s population falling into those cohorts.

With just 50 states, and a not a lot of variance to latch onto, the regression estimates are subject to considerable uncertainty.  That said, the regression coefficients for those cohorts (graphed below) pretty clearly show that the issue is mostly NOT the fading of immunity over time.  It’s that there has been a dramatic change in the ratio of total infections to total tests, as shown below.

If I go back half a year — which is when I did my last analysis — sure enough, the regression results say that for that cohort, were just over four total infections for every infection reported via PRC/antigen testing.  But as I get closer to the present (or, in this case, to March 12, 2021), that falls dramatically.  Just under 2, for the period 3 to 6 months ago, and just under 1.5 for the most recent three months prior to March 12, 2021 (the date of the seroprevalence survey).

I’m still not quite sure how much of this change is real, and how much might be an artifact of the change in the age mix of new cases.  That said, this period corresponds with the growth of the much-easier spit tests and antigen “rapid” tests.  In addition, I don’t think there is any shortage of tests any more, as there was in the early part of the pandemic in the U.S.  Given all that, the preponderance of evidence suggests that the ratio of total infections to diagnosed infections is much lower now than it was in the second half of 2020.

Implications for my herd immunity estimate.

I’ve already stated that something had to be wrong with my estimates of herd immunity or with the herd immunity model itself.  When I ran those estimates of COVID-19-immune population by state, it appeared that some states should have already passed the herd immunity threshold by a wide margin.  And some of those states would be close to any reasonable estimate of herd immunity even if there were no infections not counted via PCR/antigen test.

From Post #1131:

Here’s the problem.  Take North Dakota.  Well over half the population of that state has been immunized.  That’s a fact, and comes right out of CDC data.  More than 14% of the population has been diagnosed with a COVID-19 infection.  Again, right out of CDC data.  When I combine those two, under the assumptions of a) five total cases for every diagnosed case, and b) random overlap of the infected and vaccinated populations, then it looks like almost everyone in North Dakota ought to be immune to COVID-19 now.  Based on all those assumptions, you’d expect that 96% of the population would be immune.

But it’s even worse.  If I make the ludicrous assumption that there were never any undiagnosed COVID-19 cases, you’d still estimate that 66% of the population there was immune to COVID-19 (not shown).  Even with that gross understatement of immunity via prior infection, they’d still be right on the margin of the number that is thought to be required for herd immunity.  Toss in even a tiny bit of protection from COVID-19 hygiene (mask use, distancing, and so on) and they should still be over anybody’s plausible estimate of the requirement for herd immunity.

And yet, they don’t appear to have achieved herd immunity.  Or, at least, not with any obviousness or clarity.  Nor have any of the other states at the top of the list.  They all seem to have a low and (for the most part) stable rate of daily new COVID-19 cases.

At this point, it’s pretty clear that the five-to-one ratio that I have been using is obsolete.  It failed to keep up with reality.  Reality in this case being that tests are much easier to obtain and take now than they were in the second half of 2020.  A more reasonable round number, given the potential for blood tests to miss some cases, might be three-to-one.

In round numbers, correcting that assumption knocks 11 percentage points off the estimate of the population that is already immune to COVID-19. 

That said, even with this more conservative (and almost certainly more accurate) estimate of total infections, there are plenty of states that should exceed any reasonable estimate of the herd immunity level for the currently-circulating strains of COVID-19.  Here’s the 5/6/2021 state table, redone with this new assumption.  As you can see on the right hand column, every state on this list should have 80% of more of the population immune to COVID-19.

Returning to the just-previous post, I see Rhode Island, New Jersey, and Delaware on this list.  They were among the cluster of states with a more-than-30-percent decline in new COVID-19 cases in the last seven days.

I realize at this point that I’m grasping at straws, but maybe some states are reaching the herd immunity level right now.  My contention has been that if the end of the pandemic is driven by immunization, you won’t see the class slow tapering off of new cases.  Instead, the pandemic should end with a rapid dropoff in new cases.  (Last discussed in Post #1127).

Based on the arithmetic, a pandemic that is shut down by vaccination should end with a bang, not with a whimper.   You ought to see an accelerating rate of decline in new cases, right up to the point where there are no more cases.  That’s what I’ve been waiting to see.  Maybe we’re finally seeing it.

Post #1131: Herd immunity: Why aren’t we there yet?

Warning:  This is a long and somewhat technical post.  There aren’t really any results to speak of.  If you don’t have a strong interest in the topic of herd immunity, there’s nothing much here for you.

With that out of the way, the short answer is that we really should be getting close to herd immunity now.  But there’s no sign of it, and it’s sure starting to look overdue at this point.  I provide some state-level estimates showing that, below.

Other than saying “we’ll get there when we get there”, can I point to anything that might plausibly explain why were NOT seeing herd immunity yet?

I don’t think it’s the data. The vaccine counts are tough to argue with.  And while we can dither over exactly how many people have had COVID-19 (versus the number formally diagnosed), I don’t think that’s the hangup, either.

At this point, my guess (and it is just a guess) is that the problem is the far-too-simple model that epidemiologists use to estimate what is required for herd immunity.  I can’t really say what’s wrong with it.  But I can say that if it’s correct, and the first estimates of the infectiousness of COVID-19 (the “R-nought”) were ballpark, then it’s getting to the point where there’s really no way to explain why we’re not seeing herd immunity yet, within that standard, simple model.

My best guess?  Non-homogeneity of the population.  The standard model for herd immunity relies on an assumption of homogeneity.  In effect, it assumes that immune individuals, still-at-risk individuals, and their interactions, are all randomized.  That’s the case where, on average, many immune individuals stand between the still-vulnerable individuals and the infected individuals, stopping spread of disease.  But if that’s not true — if the natural breaks within our society result in clustering the infected and the non-immune together — it seems to me that a pandemic can keep going well past the point where the averages suggest we should have reached herd immunity.

Continue reading Post #1131: Herd immunity: Why aren’t we there yet?

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 #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 #1060: Trend updates of all sorts, and stating the obvious.

Let me start off by stating something that I think is obvious, but doesn’t get said often enough.  Even if there is a “fourth wave” of COVID-19 in the U.S., it can’t possibly be as bad as the third wave. 

Why?  Simply put, we’ve run out of bodies.  There just aren’t enough people left who aren’t already immune to COVID-19.  Between the people who’ve already had it, and the people who have been vaccinated against it, the majority of U.S. residents should be presumed to be immune to COVID-19 as it currently exists in the U.S.A.   Continue reading Post #1060: Trend updates of all sorts, and stating the obvious.

Post #1051: U.K. COVID-19 variant versus the U.S. COVID-19 vaccination rate.

Data sourced from the Helix® COVID-19 Surveillance Dashboard. Accessed at on 3/11/2021.

If you care about the details, read the caveats on the Helix COVID-19 dashboard.  This is from a sample of convenience, it’s not guaranteed to be representative of all cases (not even with in a state, let alone within the U.S. as a whole).  But I think it’s the best data available for estimating the U.S. incidence of the presumably more-infectious U.K. COVID-19 strain B.1.1.7.  And, whatever the bias in the estimate at any point in time, this should still provide a consistent estimate of the trend over time.  As of 3/8/2021 sample collection date, table “Daily Percent SGTF of Positive Samples”

U.K. COVID-19 variant as percent of new cases:

  • U.S., 32%
  • Florida, 52%

Continue reading Post #1051: U.K. COVID-19 variant versus the U.S. COVID-19 vaccination rate.

Post #1049: Trend to 3/8/2021: No change

The data source I use accidentally added 50000 cases to one state today.  After correcting that, there’s no change in the U.S. COVID-19 picture compared to yesterday.

Edit:  Nope.  Turns out that Missouri dumped about 50,000 old cases into the file as of yesterday.  (There is literally no mention of this on the Missouri state COVID-19 dashboard.  The only way to know this is to check a single nondescript state-level footnote on the NY Times Github COVID-19 data repository.)

This seems to be a catch-up for reporting of persons who tested positive via antigen testing.  I think that leaves just four states now that do not report those positive antigen tests as positives (Post #1017).   This also means that the Missouri number, going forward, should be about one-third higher than it has been historically.

Source:  Calculated from NY Times Github COVID-19 data repository, data through 3/8/2021. Continue reading Post #1049: Trend to 3/8/2021: No change

Post #1047: New cases down 77% from peak. Will the U.S. flunk the marshmallow test?


The national picture remains good. Daily new COVID-19 cases are just 23% of the peak level, and new cases are falling about 12% per week.

How much longer that will last is not yet known.

You will see experts pointing to the recent upswing in new cases in continental Europe.  They will claim that this means fourth wave in the U.S. is inevitable.

That’s not logically correct, as this post explains.  Mostly, we have a lot more immunity to COVID-19 than the typical European country does.  So the situations are not comparable.

That doesn’t mean we’re not going to have a fourth wave.  It just means that it’s still too soon to tell.

Give it a couple of weeks, and we should know one way or the other.

You’d think, in the context of a year-long pandemic, a couple more weeks of COVID-19 hygiene wouldn’t be a big deal. It’s just a question of whether the overwhelming majority of the U.S. can pass the marshmallow test.

Continue reading Post #1047: New cases down 77% from peak. Will the U.S. flunk the marshmallow test?

Post #1044: A little statistical evidence that vaccination is working in Virginia

Let me show you something that has a positive message, for a change.

As of today (3/5/2021), Virginia has fully vaccinated 30% of the oldest old (80+), and has fully or partially vaccinated more than 50% of the oldest old.

By the time you’ve got half of a population vaccinated, you ought to be able to see the impact of that on the infection rate.  And, in fact, you can.

As this post demonstrates. Continue reading Post #1044: A little statistical evidence that vaccination is working in Virginia