Tag Archives: Herd Immunity

CDC Makes a Bum Lead Steer: Alternate Reality vs. The Herd

16 Sunday May 2021

Posted by in Herd Immunity, Pandemic

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Jordan Schachtel enjoyed some schadenfreude last week when he tweeted:

“I am thoroughly enjoying the White House declaring COVID over and seeing the confused cultists having a nervous breakdown and demanding the continuation of COVID Mania.”

It’s quite an exaggeration to say the Biden Administration is “declaring COVID over”, however. They’re backpedaling, and while last week’s CDC announcement on masking is somewhat welcome, it reveals more idiotic thinking about almost everything COVID: the grotesquely excessive application of the precautionary principle (typical of the regulatory mindset) and the mentality of “zero COVID”. And just listen to Joe Biden’s tyrannical bluster following the CDC announcement:

“The rule is now simple: get vaccinated or wear a mask until you do.

The choice is yours.”

Is anyone really listening to this buffoon?Unfortunately, yes. But there’s no federal “rule”, unless your on federal property; it constitutes “guidance” everywhere else. I’m thankful our federalist system still receives a modicum of respect in the whole matter, and some states have chosen their own approaches (“Hooray for Florida”). Meanwhile, the state of the pandemic looks like this, courtesy of Andy Slavitt:

False Assertions

The CDC still operates under the misapprehension that kids need to wear masks, despite mountains of evidence showing children are at negligible risk and tend not to be spreaders. Here’s some evidence shared by Phil Kerpen on the risk to children:

The chart shows the fatality risk by age (deaths per 100,000), and then under the assumption of a 97% reduction in that risk due to vaccination, which is quite conservative. Given that kind of improvement, an unvaccinated 9 year-old child has about the same risk as a fully vaccinated 30 year-old!

The CDC still believes the unvaccinated must wear masks outdoors, but unless you’re packed in a tight crowd, catching the virus outdoors has about the same odds as a piano falling on your head. And the CDC insists that two shots of mRNA vaccine (Pfizer or Moderna) are necessary before going maskless, but only one shot of the Johnson and Johnson vaccine, even though J&J’s is less effective than a single mRNA jab!

Other details in the CDC announcement are worthy of ridicule, but for me the most aggravating are the agency’s implicit position that herd immunity can only be achieved through vaccination, and its “guidance” that the unvaccinated should be dealt with coercively, even if they have naturally-acquired immunity from an infection!

Tallying Immunity

Vaccination is only one of several routes to herd immunity, as I’ve noted in the past. For starters, consider that a significant share of the population has a degree of pre-existing immunity brought on by previous exposure to coronaviruses, including the common cold. That doesn’t mean they won’t catch the virus, but it does mean they’re unlikely to suffer severe symptoms or transmit a high viral load to anyone else. Others, while not strictly immune, are nevertheless unlikely to be sickened due to protections afforded by healthy vitamin D levels or because they are not obese. Children, of course, tend to be fairly impervious. Anyone who’s had a bout with the virus and survived is likely to have gained strong and long-lasting immunity, even if they were asymptomatic. And finally, there are those who’ve been vaccinated. All of these groups have little or no susceptibility to the virus for some time to come.

It’s not necessary to vaccinate everyone to achieve herd immunity, nor is it necessary to reach something like an 85% vax rate, as the fumbling Dr. Fauci has claimed. Today, almost 47% of the U.S. population has received at least one dose, or about 155 million adults. Here’s Kerpen’s vax update for May 14.

Another 33 million people have had positive diagnoses and survived, and estimates of seroprevalence would add perhaps another 30 million survivors. Some of those individuals have been vaccinated unnecessarily, however, and to avoid double counting, let’s say a total of 50 million people have survived the virus. Some 35 million children in the U.S. are under age 12. Therefore, even if we ignore pre-existing immunity, there are probably about 240 million effectively immune individuals without counting the remaining non-susceptibles. At the low end, based on a population of 330 million, U.S. immunity is now greater than 70%, and probably closer to 80%. That is more than sufficient for herd immunity, as traditionally understood.

The Herd Immunity Threshold

Here and in the following section I take a slightly deeper dive into herd immunity concepts.

Herd immunity was one of my favorite topics last year. I’m still drawn to it because it’s so misunderstood, even by public health officials with pretensions of expertise in the matter. My claim, about which I’m not alone, is that it’s unnecessary for a large majority of the population to be infected (or vaccinated) to limit the spread of a virus. That’s primarily because there is great variety in individuals’ degree of susceptibility, social connections, aerosol production, and viral load if exposed: call it heterogeneity or diversity if you like. Variation across individuals naturally limits a contagion relative to a homogeneous population.

Less than 1% of those who caught the virus died, while the others recovered and acquired immunity. The remaining subset of individuals most vulnerable to severe illness was thus reduced over time via acquired immunity or death. This is the natural dynamic that causes contagions to slow and ultimately peter out. In technical jargon, the virus reproduction rate “R” falls below a value of one. The point at which that happens is called the “herd immunity threshold” (HIT).

A population with lots of variation in susceptibility will have a lower HIT. Some have estimated a HIT in the U.S. as low as 15% -25%. Ultimately, total exposure will go much higher than the HIT, perhaps well more than doubling exposure, but the contagion recedes once the HIT is reached. So again, it’s unnecessary for anywhere near the full population to be immune to achieve herd immunity.

One wrinkle is that CIVID is now likely to have become endemic. Increased numbers of cases will re-emerge seasonally in still-susceptible individuals. That doesn’t contradict the discussion above regarding the HIT rate: subsequent waves will be quite mild by comparison with the past 14 months. But if the effectiveness of vaccines or acquired immunity wanes over time, or as healthy people age and become unhealthy, re-emergence becomes a greater risk.

Sub-Herd Immunity

A further qualification relates to so-called sub-herds. People are clustered by geographical, social, and cultural circles, so we should think of society not as a singular “herd”, but as a collection of sub-herds having limited cross-connectivity. The following charts are representations of different kinds of human networks, from Nathan D. Grawe’s review of “The Rules of Contagion, by Adam Kucharski:

Sub-herd members tend to have more degrees of separation from individuals in other sub-herds than within their own sub-herd. The most extreme example is the “broken network” (where contagions could not spread across sub-herds), but there are identifiable sub-herds in all of the examples shown above. Less average connectedness across sub-herds implies barriers to transmission and more isolated sub-herd contagions.

We’ve seen isolated spikes in cases in different geographies, and there have been spikes within geographies among sub-herds of individuals sharing commonalities such as race, religious affiliation, industry affiliation, school, or other cultural affiliation. Furthermore, transmission of COVID has been dominated by “super-spreader” events, which tend to occur within sub-herds. In fact, sub-herds are likely to be more homogeneous than the whole of society, and that means their HIT will be higher than we might naively calculate based on higher levels of aggregation.

We have seen local, state, or regional contagions peak and turn down when estimates of total incidence of infections reach the range of 15 – 25%. That appears to have been enough to reach the HIT in those geographically isolated cases. However, if those geographical contagions were also concentrated within social sub-herds, those sub-herds might have experienced much higher than 25% incidence by the time new infections peaked. Again, the HIT for sub-herds is likely to be greater than the aggregate population estimates implied, The upshot is that some sub-herds might have achieved herd immunity last year but others did not, which explains the spikes in new geographic areas and even the recurrence of spikes within geographic areas.

Conclusion

It’s unnecessary for 100% of the population to be vaccinated or to have pre-existing immunity. Likewise, herd immunity does not imply that no one catches the virus or that no one dies from the virus. There will be seasonal waves, though muted by the large immune share of the population. This is not something that government should try to stanch, as that would require the kind of coercion and scare tactics we’ve already seen overplayed during the pandemic. People face risks in almost everything they do, and they usually feel competent to evaluate those risks themselves. That is, until a large segment of the population allows themselves to be infantalized by public health authorities.

Note: This post also appears on The American Reveille.

COVID Now: Turning Points, Vaccines, and Mutations

20 Wednesday Jan 2021

Posted by in Coronavirus, Pandemic, Vaccinations

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The pandemic outlook remains mixed, primarily due to the slow rollout of the vaccines and the appearance of new strains of the virus. Nationwide, cases and COVID deaths rose through December. Now, however, there are several good reasons for optimism.

The fall wave of the coronavirus receded in many states beginning in November, but the wave started a bit later in the eastern states, in the southern tier of states, and in California. It appears to have crested in many of those states in January, even after a post-holiday bump in new diagnoses. As of today, Johns Hopkins reports only two states with increasing trends of new cases over the past two weeks: NH and VA, while CT and WY were flat. States shaded darker green have had larger declines in new cases.

A more detailed look at WY shows something like a blip in January after the large decline that began in November. Trends in new cases have clearly improved across the nation, though somewhat later than hoped.

While the fall wave has taken many lives, we can take some solace in the continuing decline in the case fatality rate. (This is not the same as the infection mortality rate (IFR), which has also declined. The IFR is much lower, but more difficult to measure). The CFR fell by more than half from its level in the late summer. In other words, without that decline, deaths today would be running twice as high.

Some of the CFR’s decline was surely due to higher testing levels. However, better treatments are reducing the length of hospital stays for many patients, as well as ICU admittance and deaths relative to cases. Monoclonal antibodies and convalescent plasma have been effective for many patients, and now Ivermectin is showing great promise as a treatment, with a 75% reduction in mortality according to the meta-analysis at the link.

Reported or “announced” deaths remain high, but those reports are not an accurate guide to the level or trend in actual deaths as they occur. The CDC’s provisional death reports give the count of deaths by date of death (DOD), shown below. The most recent three to four weeks are very incomplete, but it appears that actual deaths by DOD may have peaked as early as mid-December, as I speculated they might last month. Another noteworthy point: by the totals we have thus far, actual deaths peaked at about 17,000 a week, or just over 2,400 a day. This is substantially less than the “announced” deaths of 4,000 or more a day we keep hearing. The key distinction is that those announced deaths were actually spread out over many prior weeks.

A useful leading indicator of actual deaths has been the percentage of ER patients presenting COVID-like illness (CLI). The purple dots in the next CDC chart show a pronounced decline in CLI over the past three weeks. This series has been subject to revisions, which makes it much less trustworthy. A less striking decline in late November subsequently disappeared. At the time, however, it seemed to foretell a decline in actual deaths by mid-December. That might actually have been the case. We shall see, but if so, it’s possible that better therapeutics are causing the apparent CLI-deaths linkage to break down.

A more recent concern is the appearance of several new virus strains around the world, particularly in the UK and South Africa. The UK strain has reached other countries and is now said to have made appearances in the U.S. The bad news is that these strains seem to be more highly transmissible. In fact, there are some predictions that they’ll account for 30% of new cases by the beginning of March. The South African strain is said to be fairly resistant to antibodies from prior infections. Thus, there is a strong possibility that these cases will be additive, and they might or might not speedily replace the established strains. The good news is that the new strains do not appear to be more lethal. The vaccines are expected to be effective against the UK strain. It’s not yet clear whether new versions of the vaccines will be required against the South African strain by next fall.

Vaccinations have been underway now for just over a month. I had hoped that by now they’d start to make a dent in the death counts, and maybe they have, but the truth is the rollout has been frustratingly slow. The first two weeks were awful, but as of today, the number of doses administered was over 14 million, or almost 46% of the doses that have been delivered. Believe it or not, that’s an huge improvement!

About 4.3% of the population had received at least one dose as of today, according to the CDC. I have no doubt that heavier reliance on the private sector will speed the “jab rate”, but rollouts in many states have been a study in ineptitude. Even worse, now a month after vaccinations began, the most vulnerable segment of the population, the elderly, has received far less than half of the doses in most states. The following table is from Phil Kerpen. Not all states are reporting vaccinations by age group, which might indicate a failure to prioritize those at the greatest risk.

It might not be fair to draw strong conclusions, but it appears WV, FL, IN, AK, and MS are performing well relative to other states in getting doses to those most at risk.

Even with the recent increase in volume, the U.S. is running far behind the usual pace of annual flu vaccinations. Each fall, those average about 50 million doses administered per month, according to Alex Tabarrok. He quotes Youyang Gu, an AI forecaster with a pretty good track record thus far, on the prospects for herd immunity and an end to the pandemic. However, he uses the term “herd immunity” as the ending share of post-infected plus vaccinated individuals in the population, which is different than the herd immunity threshold at which new cases begin to decline. Nevertheless, in Tabarrok’s words:

“… the United States will have reached herd immunity by July, with about half of the immunity coming from vaccinations and half from infections. Long before we reach herd immunity, however, the infection and death rates will fall. Gu is projecting that by March infections will be half what they are now and by May about one-tenth the current rate. The drop will catch people by surprise just like the increase. We are not good at exponentials. The economy will boom in Q2 as infections decline.”

That sounds good, but Tabarrok also quotes a CDC projection of another 100,000 deaths by February. That’s on top of the provisional death count of 340,000 thus far, which runs 3-4 weeks behind. If we have six weeks of provisionals to go before February, with actual deaths at their peak of about 17,000 per week, we’ll get to 100,000 more actual deaths by then. For what it’s worth, I think that’s pessimistic. The favorable turns already seen in cases and actual deaths, which I believe are likely to persist, should hold fatalities below that level, and the vaccinations we’ve seen thus far will help somewhat.

Let’s Do “First Doses First”

06 Wednesday Jan 2021

Posted by in Coronavirus, Vaccinations

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Both the Pfizer and the Moderna COVID vaccines require two doses, with an effectiveness of about 95%. But a single dose may have an efficacy of about 80% that is likely to last over a number of weeks without a second dose. There are varying estimates of short-term efficacy, and but see here, here, and here. The chart above is for the Pfizer vaccine (red line) relative to a control group over days since the first dose, and the efficacy grows over time relative to the control before a presumed decay ever sets in.

Unfortunately, doses are in short supply, and getting doses administered has proven to be much more difficult than expected. “First Doses First” (FDF) is a name for a vaccination strategy focusing on delivering only first doses until a sufficient number of the highly vulnerable receive one. After that, second doses can be administered, perhaps within some maximum time internal such as 8 – 12 weeks. FDF doubles the number of individuals who can be vaccinated in the short-term with a given supply of vaccine. Today, Phil Kerpen posted this update on doses delivered and administered thus far:

Dosing has caught up a little, but it’s still lagging way behind deliveries.

As Alex Tabbarok points out, FDF is superior strategy because every two doses create an average of 1.6 immune individuals (2 x 0.8) instead of just 0.95 immune individuals. His example involves a population of 300 million, a required herd immunity level of two-thirds (higher than a herd immunity threshold), and an ability to administer 100 million doses per month. Under a FDF regime, you’ve reached Tabarrok’s “herd immunity” level in two months. (This is not to imply that vaccination is the only contributor to herd immunity… far from it!) Under the two-dose regime, you only get halfway there in that time. So FDF means fewer cases, fewer deaths, shorter suspensions of individual liberty, and a faster economic recovery.

An alternative that doubles the number of doses available is Moderna’s half-dose plan. Apparently, their tests indicate that half doses are just as effective as full doses, and they are said to be in discussions with the FDA and Operation Warp Speed to implement the half-dose plan. But the disadvantage of the half-dose plan relative to FDF is that the former does not help to overcome the slow speed with which doses are being administered.

Vaccine supplies are bound to increase dramatically in coming months, and the process of dosing will no doubt accelerate as well. However, for the next month or two, FDF is too sensible to ignore. While I am not a fan of all British COVID policies, their vaccination authorities have recommended an FDF approach as well as allowing different vaccines for first and second doses.

Fauci Flubs Herd Immunity

03 Sunday Jan 2021

Posted by in Coronavirus, Herd Immunity, Public Health, Vaccinations

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Anthony Fauci has repeatedly increased his estimate of how much of the population must be vaccinated to achieve what he calls herd immunity, and he did it again in late December. This series of changes, and other mixed messages he’s delivered in the past, reveal Fauci to be a “public servant” who feels no obligation to level with the public. Instead, he crafts messages based on what he believes the public will accept, or on his sense of how the public must be manipulated. For example, by his own admission, his estimates of herd immunity have been sensitive to polling data! He reasoned that if more people reported a willingness to take a vaccine, he’d have flexibility to increase his “public” estimate of the percentage that must be vaccinated for herd immunity. Even worse, Fauci appears to lack a solid understanding of the very concept of herd immunity.

Manipulation

There is so much wrong with his reasoning on this point that it’s hard to know where to start. In the first place, why in the world would anyone think that if more people willingly vaccinate it would imply that even more must vaccinate? And if he felt that way all along it demonstrates an earlier willingness to be dishonest with the public. Of course, there was nothing scientific about it: the series of estimates was purely manipulative. It’s almost painful to consider the sort of public servant who’d engage in such mental machinations.

Immunity Is Multi-Faceted

Second, Fauci seemingly wants to convince us that herd immunity is solely dependent on vaccination. Far from it, and I’m sure he knows that, so perhaps this too was manipulative. Fauci intimates that COVID herd immunity must look something like herd immunity to the measles, which is laughable. Measles is a viral infection primarily in children, among whom there is little if any pre-immunity. The measles vaccine (MMR) is administered to young children along with occasional boosters for some individuals. Believe it or not, Fauci claims that he rationalized a requirement of 85% vaccination for COVID by discounting a 90% requirement for the measles! Really???

In fact, there is substantial acquired pre-immunity to COVID. A meaningful share of the population has long-memory, cross-reactive T-cells from earlier exposure to coronaviruses such as the common cold. Estimates range from 10% to as much as 50%. So if we stick with Fauci’s 85% herd immunity “guesstimate”, 25% pre-immunity implies that vaccinating only 60% of the population would get us to Fauci’s herd immunity goal. (Two qualifications: 1) the vaccines aren’t 100% effective, so it would take more than 60% vaccinated to offset the failure rate; 2) the pre-immune might not be identifiable at low cost, so there might be significant overlap between the pre-immune and those vaccinated.)

Conceptual Confusion

Vaccinations approaching 85% would be an extremely ambitious goal, especially if it is recommended annually or semi-annually. It would be virtually impossible without coercion. While more than 91% of children are vaccinated for measles in the U.S., it is not annual. Thus, measles does not offer an appropriate model for thinking about herd immunity to COVID. Less than half of adults get a flu shot each year, and somewhat more children.

Fauci’s reference to 85% – 90% total immunity is different from the concept of the herd immunity threshold (HIT) in standard epidemiological models. The HIT, often placed in the range of 60% – 70%, is the point at which new infections begin to decline. More infections occur above the HIT but at a diminishing rate. In the end, the total share of individuals who become immune due to exposure, pre-immunity or vaccination will be greater than the HIT. The point is, however, that reaching the HIT is a sufficient condition for cases to taper and an end to a contagion. If we use 65% as the HIT and pre-immunity of 25%, only 40% must be vaccinated to reach the HIT.

Heterogeneity

A recent innovation in epidemiological models is the recognition that there are tremendous differences between individuals in terms of transmissibility, pre-immunity, and other factors that influence the spread of a particular virus, including social and business arrangements. This kind of heterogeneity tends to reduce the effective HIT. We’ve already discussed the effect of pre-immunity. Suppose that certain individuals are much more likely to transmit the virus than others, like so-called super-spreaders. They spur the initial exponential growth of a contagion, but there are only so many of them. Once infected, no one else among the still-susceptible can spread the virus with the same force.

Researchers at the Max Planck Institute (and a number of others) have gauged the effect of introducing heterogeneity to standard epidemiological models. It is dramatic, as the following chart shows. The curves simulate a pandemic under different assumptions about the degree of heterogeneity. The peak of these curves correspond to the HIT under each assumption (R0 refers to the initial reproduction number from infected individuals to others).

Moderate heterogeneity implies a HIT of only 37%. Given pre-immunity of 25%, only an additional 12% of the population would have to be infected or vaccinated to prevent a contagion from gaining a foothold for the initial exponential stage of growth. Fauci’s herd immunity figure obviously fails to consider the effect of heterogeneity.

How Close To the HIT?

We’re not as far from HITs as Fauci might think, and a vaccination goal of 85% is absurd and unnecessary. The seasonal COVID waves we’ve experienced thus far have faded over a period of 10-12 weeks. Estimates of seroprevalence in many localities reached a range of 15% – 25% after those episodes, which probably includes some share of those with pre-immunity. To reach the likely range of a HIT, either some additional pre-immunity must have existed or the degree of heterogeneity must have been large in these populations.

But if that’s true, why did secondary waves occur in the fall? There are a few possibilities. Of course, some areas like the upper Midwest did not experience the springtime wave. But in areas that suffered a recurrance, perhaps the antibodies acquired from infections did not remain active for as long as six months. However, other immune cells have longer memories, and re-infections have been fairly rare. Another possibility is that those having some level of pre-immunity were still able to pass live virus along to new hosts. But this vector of transmission would probably have been quite limited. Pre-immunity almost surely varies from region to region, so some areas were not as firmly above their HITs as others. It’s also possible that infections from super-spreaders were concentrated within subsets of the population even within a given region, in certain neighborhoods or among some, but not all, social or business circles. Therefore, some subsets or “sub-herds” achieved a HIT in the first wave, but it was unnecessary for other groups. In other words, sub-herds spared in the first wave might have suffered a contagion in a subsequent wave. And again, reinfections seem to have been rare. Finally, there is the possibility of a reset in the HIT in the presence of a new, more transmissible variant of the virus, as has become prevalent in the UK, but that was not the case in the fall.

Fragility

Tyler Cowen has mentioned another possible explanation: so-called “fragile” herd immunity. The idea is that any particular HIT is dependent on the structure of social relations. When social distancing is widely practiced, for example, the HIT will be lower. But if, after a contagion recedes, social distancing is relaxed, it’s possible that the HIT will take a higher value at the onset of the next seasonal wave. Perhaps this played a role in the resurgence in infections in the fall, but the HIT can be reduced via voluntary distancing. Eventually, acquired immunity and vaccinations will achieve a HIT under which distancing should be unnecessary, and heterogeneity suggests that shouldn’t be far out of reach.

Conclusion

Anthony Fauci has too often changed his public pronouncements on critical issues related to management of the COVID pandemic. Last February he said cruises were fine for the healthy and that most people should live their lives normally. Oops! Then came his opinion on the limited effectiveness of masks, then a shift to their necessity. His first position on masks has been called a “noble lie” intended to preserve supplies for health care workers. However, Fauci was probably repeating the standing consensus at that point (and still the truth) that masks are of limited value in containing airborne pathogens.

This time, Fauci admitted to changing his estimate of “herd immunity” in response to public opinion, a pathetic approach to matters of public health. What he called herd immunity was really an opinion about adequate levels of vaccination. Furthermore, he neglected to consider other forms of immunity: pre-existing and already acquired. He did not distinguish between total immunity and the herd immunity threshold that should guide any discussion of pandemic management. He also neglected the significant advances in epidemiological modeling that recognize the reality of heterogeneity in reducing the herd immunity threshold. The upshot is that far fewer vaccinations are needed to contain future waves of the pandemic than Fauci suggests.

Harbingers of COVID Fade, But Not the Pretense for Hysteria

17 Thursday Dec 2020

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My pre-Thanksgiving optimism about a crest in the fall wave of the coronavirus has been borne out for the Midwest and Mountain states in the U.S. These regions were the epicenter of the fall wave through October and most of November, but new cases in those states have continued to decline. Cases in a number of other states began to climb in November, however, contributing to a continuing rise in total new cases nationally. Some of these states are still in the throes of this wave, with the virus impacting subsets of the population that were relatively unscathed up till now.

My disclaimer: COVID is obviously a nasty virus. I don’t want to get it. However, on the whole, it is not a cataclysm on the order of many pandemics of the past. In fact, excess deaths this year will add just over 10% to projections of total deaths based on a five-year average. That level puts us in line with average annual deaths of about twenty years ago. And many of those excess deaths have been caused by our overreaction to the pandemic, not by the virus itself. As my endocrinologist has said, this is the greatest overreaction in all medical history. Unfortunately, a fading pandemic does not mean we can expect an end to the undue panic, or pretense for panic, on the part of interventionists.

This post will focus largely on trends in newly diagnosed COVID cases. I have been highly critical of our testing regime and COVID case counts because the most prominent diagnostic test (PCR) falsely identifies a large number of uninfected individuals as COVID-positive. However, case numbers are widely tracked and it’s fairly easy to find information across geographies for comparison. Deflate all the numbers by 30% if you want, or by any other factor, but please indulge me because I think the trends are meaningful, even if the absolute level of cases is inflated.

I’ll start with the good news and work my way down to states in which cases are still climbing (all of the following charts are from @Humble_Analysis (PLC)). The first chart is for the Great Plains, where cases peaked a little before Thanksgiving and have continued to fall since then. That peak came about six weeks after it began in earnest and cases have faded over the last four weeks.

Next we have the Mountain states, where again, cases peaked around Thanksgiving, though Idaho saw a rebound after the holiday. You’ll see below that a number of states had a distinct drop in new cases during the week of Thanksgiving. There was somewhat of a pause in testing during that week, so the subsequent rebounds are largely due to a “catch-up” at testing sites, rather than some kind of Thanksgiving-induced spike in infections.

Back to the Mountain region, the peak came an average of about six or seven weeks into the wave, but the duration of the wave appears to have been longer in Montana and Wyoming.

Here are the Southern Plain states, where cases plateaued around Thanksgiving (though cases in Missouri have clearly declined from their peak). In this region, case counts accelerated in October after a slow climb over the summer.

The situation is somewhat similar in the Midwest. where cases have generally plateaued. There were some post-Thanksgiving rebounds in several states, especially Tennessee. The wave began a little later in this region, in mid- to late October, and it is now seven to eight weeks into the wave, on average.

Here are the Mid-Atlantic states, which may be showing signs of a peak, though North Carolina has had the greatest caseload and is still climbing. These states are about seven weeks into the wave, on average.

The Northeast also shows signs of a possible peak and is about seven weeks into the wave, except for Rhode Island, which saw an earlier onset and the most severe wave among these states.

And finally we have the South, which is defined quite broadly in PLC’s construction. It’s a mixed bag, with a few states showing signs of a peak after about seven weeks. However, cases are still climbing in several states, notably California and Florida, among a few others.

Oregon and Washington were skipped, but they appear as the Pacific NW in the following chart, along with aggregations for all the other regions. Maine is Part of the “Rural NE”, which was also skipped. The fall wave can be grouped roughly into two sets of regions: those in which waves began in late September or early October, and those where waves began in early to mid-November. The first group has moved beyond a peak or at least has plateaued. The latter group may be reaching peaks now or one hopes very soon. It seems to take about seven weeks to reach the peak of these regional waves, so a late December peak for the latter group would be consistent.

Justin Hart has a take on the duration of these waves, but he does so in terms of the share of emergency room (ER) visits in which symptoms of COVID-like illness (CLI) are presented. CLI tends to precede case counts slightly. Hart puts the duration of these waves at eight to ten weeks, but that’s a judgement call, and I might put it a bit longer using caseloads as a guide. Still, this color-coded chart from Hart is interesting.

If this sort of cyclical duration holds up, it’s consistent with the view that cases in many of the still “hot” states should be peaking this month.

Aggregate cases for the U.S. appear below. The growth rate of new cases has slowed, and the peak is likely to occur soon. However, because it combines all of the regional waves, the duration of the wave nationwide will appear to be greater than for the individual regions. COVID-attributed deaths are also plotted, but they are reported deaths, not by date of death (DOD) or actual deaths, as I sometimes call them. Deaths by DOD are available only with a lag. As always, some of the reported deaths shown below occurred weeks before their reported date. Actual deaths were still rising as of late November, and are likely still rising. However, another indicator suggests they should be close to a peak.

A leading indicator of actual deaths I’ve discussed in the past now shows a more definitive improvement than it did just after Thanksgiving, as the next chart shows. This is the CLI share discussed above. An even better predictor of COVID deaths by actual DOD is the sum of CLI and the share of ER patients presenting symptoms of influenza-like illness (ILI), but ILI has been fairly low and stable, so it isn’t contributing much to changes in trend at the moment. There has been about a three-week lead between movements in CLI+ILI and COVID deaths by DOD.

(The reason the sum, CLI+ILI, has been a better predictor than CLI alone is because for some individuals, there are similarities in the symptoms of COVID and the flu.)

The chart shows that CLI peaked right around the Thanksgiving holiday (and so did CLI+ILI), but it remained on something of a plateau through the first week of December before declining. Some of the last few days on this chart are subject to revision, but the recent trend is encouraging. Allowing for a three-week lead, this indicates that peak deaths by DOD should occur around mid-December, but we won’t know exactly until early to mid-January. To be conservative, we might say the latter half of December will mark the peak in actual deaths.

The regional COVID waves this summer and fall seem to have run their course within 10 – 12 weeks. Several former hot spots have seen cases drop since Thanksgiving after surges of six to seven weeks. However, there are several other regions with populous states where the fall wave is still close to “mid-cycle”, as it were, showing signs of possible peaks after roughly seven weeks of rising cases. The national CLI share peaked around Thanksgiving, but it did not give up much ground until early December. That suggests that actual deaths (as opposed to reported deaths), at least in some regions, will peak around the time of the winter solstice. Let’s hope it’s sooner.

Successive waves within a region seem to reach particular subsets of the population with relatively few reinfections. The 10 – 12 week cycle discussed above is sufficient to achieve an effective herd immunity within these subsets. But once again, a large share of the vulnerable, and a large share of COVID deaths, are still concentrated in the elderly, high-risk population and in care homes. The vaccine(s) currently being administered to residents of those homes are likely to hasten the decline in COVID deaths beginning sometime in January, perhaps as early as mid-month. By then, however, we should already see a decline underway as this wave of the virus finally burns itself out. As vaccines reach a larger share of the population through the winter and spring, the likelihood of additional severe waves of the virus will diminish.

Lest there be any misunderstanding, the reasons for the contagion’s fade to come have mostly to do with reaching the effective herd immunity threshold within afflicted subsets of the population (sub-herds). Social distancing certainly plays a role as well. Nearly all of that is voluntary, though it has been encouraged by panicked pronouncement by certain public officials and the media. Direct interventions or lockdown measures are in general counter-productive, however, and they create a death toll of their own. Unfortunately, the fading pandemic might not rein-in the curtailment of basic liberties we’ve witnessed this year.

Post-Script: Let’s hope the side effects of the vaccines are not particularly severe in the elderly. That’s a little uncertain, because that sub-population was not tested in very high numbers.

Auspicious COVID News for Thanksgiving

25 Wednesday Nov 2020

Posted by in Coronavirus, Herd Immunity

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There are some hints of good news on the spread of the coronavirus in a few of the “hot spots“ that developed this fall. This could be very good news, but it’s a bit too early to draw definitive conclusions.

The number of new cases plateaued in Europe a few weeks ago. Of course, Europe’s average latitude is higher than in most of the U.S., and the seasonal spread began there a little earlier. It makes sense that it might ebb there a bit sooner than in the U.S. as well.

In the U.S., cases shot up in the upper Midwest four to six weeks ago, depending on the state. Now, however, new cases have turned down in Iowa, Nebraska, North Dakota, South Dakota, and Wisconsin (first chart below), and they appear to have plateaued in Illinois, Kansas, Minnesota, and Missouri (second chart below, but ending a few days earlier). These are the hottest of the recent hot states.

These plateaus and declines were preceded by a decline in the growth rates of new cases around 10 days ago, shown below.

The timing of these patterns roughly correspond to the timing of the spread in other regions earlier in the year. It’s been suggested that after seroprevalence reaches levels of around 15% – 25% that individuals with new antibodies, together with individuals having an existing pre-immunity from other coronaviruses, is enough to bring the virus reproduction rate (R) to a value of one or less. That means a breach of the effective herd immunity threshold. It’s possible that many of these states are reaching those levels. Of course, this is very uncertain, but the patterns are certainly encouraging.

Deaths lag behind new infections, and it generally takes several weeks before actual deaths by date-of-death are known with any precision. However, we might expect deaths to turn down within two to three weeks.

Deaths by date-of-death are strongly associated with emergency room patients from three weeks prior who presented symptoms of COVID-like illness (CLI) or influenza-like illness ((ILI). The following chart shows CLI and ILI separately for the entire U.S. (ILI is the lowest dashed line), but the last few observations of both series, after a peak on November 15th, suggest a downturn in CLI + ILI. If the relationship holds up, actual U.S. deaths by date-of-death should peak around December 7th, though we won’t know precisely until early in the new year.

As a side note, it continues to look like the flu season will be exceptionally mild this year. See the next chart. That’s tremendous because it should take some of the normal seasonable pressure off health care resources.

So Happy Thanksgiving!

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Note: I saved all those charts over the last few days but lost track of the individual sources on Twitter. I’m too lazy and busy to go back and search through Twitter posts, so instead I’ll just list a few of my frequent sources here with links to recent posts, which are not necessarily apropos of the above: Don Wolt, Justin Hart, AlexL, The Ethical Skeptic, Aaron Ginn, and HOLD2.

COVID and Hospital Capacity

15 Sunday Nov 2020

Posted by in Health Care, Pandemic

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The fall wave of the coronavirus has brought with it an increase in COVID hospitalizations. It’s a serious situation for the infected and for those who care for them. But while hospital utilization is rising and is reaching tight conditions in some areas, claims that it is already a widespread national problem are without merit.

National and State Hospital Utilization

The table below shows national and state statistics comparing beds used during November 1-9 to the three-year average from 2017 – 19, from Justin Hart. There are some real flaws in the comparison: one is that full-year averages are not readily comparable to particular times of the year, with or without COVID. Nevertheless, the comparison does serve to show that current overall bed usage is not “crazy high” in most states, as it were. The increase in utilization shown in the table is highest in IA, MT, NV, PA, VT, and WI, and there are a few other states with sizable increases.

Another limitation is that the utilization rates in the far right column do not appear to be calculated on the basis of “staffed” beds, but total beds. The U.S. bed utilization rate would be 74% in terms of staffed beds.

Average historical hospital occupancy rates from Statista look like this:

Again, these don’t seem to be calculated on the basis of staffed beds, but current occupancies are probably higher now based on either staffed beds or total beds.

As of November 11th, a table available at HealthData.gov indicates that staffed bed utilization in the U.S. is at nearly 74%, with ICU utilization also at 74%. As the table above shows, states vary tremendously in their hospital bed utilization, a point to which I’ll return below.

COVID patients were using just over 9% of of all staffed beds and just over 19% of ICU beds as of November 11th. One caveat on the reported COVID shares you’ll see for dates going forward: the CDC changed its guidelines on counting COVID hospitalizations as of November 12th. It is now a COVID patient’s entire hospital stay, rather than only when a patient is in isolation with COVID. That might be a better metric if we can trust the accuracy of COVID tests (and I don’t), but either way, the change will cause a jump in the COVID share of occupied beds.

Interpreting Hospital Utilization

Many issues impinge on the interpretation of hospital utilization rates:

First, cases and utilization rates are increasing, which is worrisome, but the question is whether they have already reached crisis levels or will very soon. The data doesn’t suggest that is the case in the aggregate, but there certainly there are hospitals bumping up against capacity constraints in some parts of the country.

Second, occupancies are increasing due to COVID patients as well as patients suffering from lockdown-related problems such as self-harm, psychiatric problems, drug abuse, and conditions worsened by earlier deferrals of care. We can expect more of that in coming weeks.

Third, lockdowns create other hospital capacity issues related to staffing. Health care workers with school-aged children face the daunting task of caring for their kids and maintaining hours on jobs for which they are critically needed.

Fourth, there are capacity issues related to PPE and medical equipment that are not addressed by the statistics above. Different uses must compete for these resources within any hospital, so the share of COVID admissions has a strong bearing on how the care of other kinds of patients must be managed.

Fifth, some of the alarm is purely case-driven: all admissions are tested for COVID, and non-COVID admissions often become COVID admissions after false-positive PCR tests, or simply due to the presence of mild COVID with a more serious condition or injury. However, severe COVID cases have an outsized impact on utilization of staff because their care is relatively labor-intensive.

Sixth, there are reports that the average length of COVID patient stays has decreased markedly since the spring (it is hard to find nationwide figures), but it is also increasingly difficult to find facilities for post-acute care required for some patients on discharge. Nevertheless, if improved treatment reduces average length of stay, it helps hospitals deal with the surge.

Finally, thus far, the influenza season has been remarkably light, as the following chart from the CDC shows. It is still early in the season, but the near-complete absence of flu patients is helping hospitals manage their resources.

St. Louis Hotspot

The St. Louis metro area has been proclaimed a COVID “hotspot” by the local media and government officials, which certainly doesn’t make St. Louis unique in terms of conditions or alarmism. I’m curious about the data there, however, since it’s my hometown. Here is hospital occupancy on the Missouri side of the St. Louis region:

It seems this chart is based on total beds, not staffed beds, However, one of the interesting aspects of this chart is the variation in capacity over time, with several significant jumps in the series. This has to do with data coverage and some variation in daily reporting. Almost all of these data dashboards are relatively new, so their coverage has been increasing, but generally in fits and starts. Reporting is spotty on a day-to-day basis, so there are jagged patterns. And of course, capacity can vary from day-to-day and week-to-week — there is some flexibility in the number of beds that can be made available.

The share of St. Louis area beds in use was 61% as of November 11th (preliminary). COVID patients accounted for 12% of hospital beds. ICU utilization in the St. Louis region was a preliminary 67% as of Nov. 11, with COVID patients using 29% of ICU capacity (which is quite high). Again, these figures probably aren’t calculated on the basis of “staffed” beds, so actual hospital-bed and ICU-bed utilization rates could be several percentage points higher. More importantly, it does not appear that utilization in the St. Louis area has trended up over the past month.

At the moment, the St. Louis region appears to have more spare hospital capacity than the nation, but COVID patients are using a larger share of all beds and ICU beds in St. Louis than nationwide. So this is a mixed bag. And again, capacity is not spread evenly across hospitals, and it’s clear that hospitals are under pressure to manage capacity more actively. In fact, hospitals only have so many options as the share of COVID admissions increases: divert or discharge COVID and non-COVID patients, defer elective procedures, discharge COVID and non-COVID patients earlier, allow beds to be more thinly staffed and/or add temporary beds wherever possible.

Closing Thoughts

Anyone with severe symptoms of COVID-19 probably should be hospitalized. The beds must be available, or else at-home care will become more commonplace, as it was for non-COVID maladies earlier in the pandemic. A continued escalation in severe COVID cases would require more drastic steps to make hospital resources available. That said, we do not yet have a widespread capacity crisis, although that’s small consolation to areas now under stress. And a few of the states with the highest utilization rates now have been rather stable in terms of hospitalizations — they already had high average utilization rates, which is potentially dangerous.

COVID is a seasonal disease, and it’s no surprise that it’s raging now in areas that did not experience large outbreaks in the spring and summer. And those areas that had earlier outbreaks have not had a serious surge this fall, at least not yet. My expectation and hope is that the midwestern and northern states now seeing high case counts will soon reach a level of prevalence at which new infections will begin to subside. And we’re likely to see a far lower infection fatality rate than experienced in the Northeast last spring.

Predicted November COVID Deaths

08 Sunday Nov 2020

Posted by in Pandemic, Public Health

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Reported COVID deaths do not reflect deaths that actually occurred in the reporting day or week, as I’ve noted several times. Here is a nice chart from @tlowdon on Twitter showing the difference between reported deaths and actual deaths for corresponding weeks. The blue bars are weekly deaths reported by the COVID Tracking Project. The solid orange bars are the CDC’s “provisional” deaths by actual week of death, which is less than complete for recent weeks because of lags in reporting. Still, it’s easy to see that reported deaths have overstated actual deaths each week since late August.

I should note that the orange bars represent deaths that involved COVID-19, though a COVID infection might not have actually killed them. This CDC report, updated on November 4th, shows the importance of co-morbidities, which in many cases are the actual cause of death according to pre-COVID, CDC guidance on death certificates.

Leading Indicators

Researchers have studied several measures in an effort to find leading indicators of COVID deaths. The list includes new cases diagnosed (PCR positivity) and the percentage of emergency room visits presenting symptoms of COVID-like illness (%CLI). These indicators are usually evaluated after shifting them in time by a few weeks in order to observe correlations with COVID deaths a few weeks later. Interestingly, @tlowdon reports that the best single predictor of actual COVID deaths over the course of a few weeks is the sum of the %CLI and the percentage of ER patients presenting symptoms of influenza-like illness (%ILI). Perhaps adding %ILI to %CLI strengthens the correlation because the symptoms of the flu and COVID are often mistaken for one another.

The chart below reproduces the orange bars from above representing deaths at actual dates of death. Also plotted are the %Positivity from COVID tests (shifted forward 2 weeks), %CLI (3 weeks), the %ILI (3 weeks), and the sum of %CLI and %ILI (3 weeks, the solid blue line). My guess is that %ILI contributes to the correlation with deaths mainly because %ILI’s early peak (which occurred in March) led the peak in deaths in April. Otherwise, there is very little variation in %ILI. That might change with the current onset of the flu season, but as I noted in my last post, the flu has been very subdued since last winter.

What About November?

So where does that leave us? The chart above ends with our leading indicator, CLI + ILI, brought forward from the first half of October. What’s happened to CLI + ILI since then? And what does that tell us to expect in November? The chart below is from the CDC’s web site. The red line is %CLI and the yellow line is %ILI. The sum of the two isn’t shown. However, there is no denying the upward trend in CLI, though the slope of CLI + ILI would be more moderate.

As of 10/31, CLI + ILI has increased by almost 40% since it’s low in early October. If the previous relationship holds up, that implies an increase of almost 40% in actual weekly COVID deaths from about 4,000 per week to about 5,500 per week by November 21 (a little less than 800 per day).

FiveThirtyEight has a compilation of 13 different forecast models with projections of deaths by the end of November. The estimate of 5,500 per week by November 21, or perhaps slightly less per week over the full month of November, would put total COVID deaths at the top of the range of the MIT, UCLA, Iowa State, and University of Texas models, but below or near the low end of ranges for eight other models. However, those models are based on reported deaths, so the comparison is not strictly valid. Reported deaths are still likely to exceed actual deaths by the end of November, and the actual death prediction would be squarely in the range of multiple reported death predictions. That reinforces the expectation an upward trend in actual deaths.

Third Wave States

States in the upper Midwest and upper Mountain regions have had the largest increases in cases per capita over the past few weeks. Using state abbreviations, the top ten are ND, SD, WI, IA, MT, NE, WY, UT, IL, and MN, with ID at #11 (according to the CDC’s COVID Data Tracker). One factor that might mediate the increase in cases, and ultimately deaths, is the possibility of early herd immunity: in the earlier COVID waves, the increase in infections abated once seroprevalence (the share of the population with antibodies from exposure) reached a level of 15% to 25%.

Unfortunately, estimates of seroprevalence by state are very imprecise. Thus far, reliable samples have been limited to states and metro areas that had heavy infections in the first and second waves. One rule of thumb, however, is that seroprevalence is probably less than 10x the cumulative share of a population having tested positive. To be very conservative, let’s assume a seroprevalence of four times cumulative cases. On that basis, half the states in the “top ten” listed above would already have seroprevalence above 15%. Those states are ND, SD, WI, IA, and NE. The others are mostly in a range of 12% to 15%, with MI coming in the lowest at about 9%.

This gives some cause for optimism that the wave in these states and others will abate fairly soon, but there are a number of uncertainties: first, the estimates of seroprevalence above, while conservative, are very imprecise, as noted above; second, the point at which herd immunity might cause the increase in new cases to begin declining is real guesswork (though we might have confirmation in a few states before long); third, we are now well into the fall season, with lower temperatures, lower humidity, less direct sunlight, and diminishing vitamin D levels. We do not have experience with COVID at this time of year, so we don’t know whether the patterns observed earlier in the year will be repeated. If so, new cases might begin to abate in some areas in November, but that probably wouldn’t be reflected in deaths until sometime in December. And if the flu comes back with a corresponding increase in CLI + ILI, then we’d expect further increases in actual deaths attributed to COVID. That is only a possibility given the weakness in flu numbers in 2020, however.

Closing Thoughts

I was excessively optimistic about the course of the pandemic in the U.S. in the spring. While this post has been moderately pessimistic, I believe there are reasons to expect fewer deaths than previous relationships would predict. We are far better at treating COVID now, and the vulnerable are taking precautions that have reduced their incidence of infections relative to younger and healthier cohorts. So if anything, I think the forecasts above will err on the high side.

COVID Trends and Flu Cases

05 Thursday Nov 2020

Posted by in Pandemic

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Writing about COVID as a respite from election madness is very cold comfort, but here goes….

COVID deaths in the U.S. still haven’t shown the kind of upward trend this fall that many had feared. It could happen, but it hasn’t yet. In the chart above, new cases are shown in brown (along with the rolling seven-day average), while deaths (on the right axis) are shown in blue. It’s been over six weeks since new case counts began to rise, but deaths have risen for about two weeks, and it’s been gradual relative to the first two waves. Either the average lag between diagnosis and death is much longer than earlier in the year, or the current “casedemic” is much less deadly, or perhaps both. It could change. And granted, this is national data; states in the midwest have had the strongest trends in cases, especially the upper midwest, as well as stronger trends in hospitalizations and deaths. Most of those areas had milder experiences with the virus in the spring and summer.

Lagged Reporting

What’s tricky about this is that both case reports and death reports in the chart above are significantly lagged. A COVID test might not take place until several days after infection (if at all), and sometimes not until hospitalization or death. Then the test result might not be known for several days. However, the greater availability of tests and faster turnaround time have almost certainly shortened that lag.

Deaths are reported with an even a greater delay, though you wouldn’t know it from listening to the media or some of the organizations that track these statistics, such as Johns Hopkins University and the COVID Tracking Project. Thus far, they only tell you what’s reported on a given day. This article from Rational Ground does a good job of explaining the issue and the distortion it causes in discerning trends.

Deaths by actual date-of-death

I’ve reported on the issue of lagged COVID deaths myself. The following graph from Justin Hart is a clear presentation of the reporting delays.

Reported deaths for the most recent week (10/24) are shown in dark blue, and those deaths were spread over a number of prior weeks. Actual deaths in a given week are represented by a “stack” of deaths reported later, in subsequent weeks. One word of caution: actual deaths in the most recent weeks are “provisional”, and more will be added in subsequent reporting weeks. Hence the steep drop off for the 10/17 and 10/24 reporting weeks.

Going back three or four weeks, it’s clear that actual deaths continued to decline into October. Unfortunately, that doesn’t tell us much about the recent trend or whether actual deaths have started to rise given the increase in new cases. I have seen a new weekly update with the deaths by actual date of death, but it is not “stacked” by reporting week. However, it does show a slight increase in the week of 10/10, the first weekly increase since the end of June. So perhaps we’ll see an uptick more in-line with the earlier lags between diagnosis and death, but that’s far from certain.

Another important point is that the number of deaths each week, and each day, are not as high as reported by the media and the popular tracking sites. How often have you heard “more than 1,000 people a day are dying”. That’s high even for weekly averages of reported deaths. As of three weeks ago, actual daily deaths were running at about 560. That’s still very high, but based on seroprevalence estimates (the actual number of infections from the presence of antibodies), the infection fatality keeps dropping toward levels that are comparable to the flu at ages less than 65.

Where is the flu?

Speaking of the flu, this chart from the World Health Organization is revealing: the flu appears to have virtually disappeared in 2020:

It’s still very early in the northern flu season, but the case count was very light this summer in the Southern Hemisphere. There are several possible explanations. One favored by the “lockdown crowd” is that mitigation efforts, including masks and social distancing, have curtailed the flu bug. Not just curtailed … quashed! If that’s true, it’s more than a little odd because the same measures have been so unsuccessful in curtailing COVID, which is transmitted the same way! Also, these measures vary widely around the globe, which weakens the explanation.

There are other, more likely explanations: perhaps the flu is being undercounted because COVID is being overcounted. False positive COVID tests might override the reporting of a few flu cases, but not all diagnoses are made via testing. Other respiratory diseases can be mistaken for the flu and vice versus, and they are now more likely to be diagnosed as COVID absent a test — and as the joke goes, the flu is now illegal! And another partial explanation: it is rare to be infected with two viruses at once. Thus, COVID is said to be “crowding out” the flu.

Waiting for data

There is other good news about transmission, treatment, and immunity, but I’ll devote another post to that, and I’ll wait for more data. For now, the “third wave” appears to be geographically distinct from the first two, as was the second wave from the first. This suggests a sort of herd immunity in areas that were hit more severely in earlier waves. But the best news is that COVID deaths, thus far this fall, are not showing much if any upward movement, and estimates of infection fatality rates continue to fall.

COVID Immunity, Herd By Herd

01 Tuesday Sep 2020

Posted by in Coronavirus, Herd Immunity

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Too many public health authorities remain in denial, but epidemiologists are increasingly convinced that heterogeneity implies a coronavirus herd immunity threshold (HIT) that is greatly reduced from traditional models and estimates. HIT is the share of the population that must be infected before the contagion begins to recede (and the transmission ratio R falls below one). Traditional models, based on three classes of individuals (Susceptibles, Infectives, and Recovered – SIR), predict a HIT of 60% or more. However, models that incorporate variation in susceptibility, transmissibility, and occupational or social behavior reduce the HIT substantially. Many of these more nuanced models show that the HIT could be in a range of just 15% to 25%. If that is the case, many regions are already there!

For background, I refer you to the first post I wrote about heterogeneity in late March, more detailed thoughts from early May, examples and more information on the literature later in May. I’ve referenced it repeatedly in other posts since then. And now, more than five months later, even the slow kids at the New York Times have noticed. The gist of it: if not everyone is equally susceptible, for example, a smaller share of the population needs to be “immunized via infection” to taper the spread of the virus.

Some supporting evidence appears in the charts below, courtesy of Kyle Lamb on Twitter. The first chart shows a seven-day average of C19 cases per million of population for ten states that reached an estimated 10% antibodies. These antibodies confer at least short-term immunity against C19. Most of these states saw cases/m climb at least through the day when the 10% level was reached, though Rhode Island appears to have been an exception.

The second chart shows the seven-day average of cases/m in the same states starting seven days after the 10% immunity level was reached. I’d prefer to see the days in the interim as well, but the changes in trend are still noteworthy. All of these states except Louisiana had a downturn in the seven-day average of new cases within a few weeks of breaching the 10% infection level (Louisiana had distinct and non-coincident outbreaks in different parts of the state). These striking similarities suggest that things turned as the infection level reached 15% or more, consistent with many of the epidemiological models incorporating heterogeneity.

Next, take a look at the states in which C19 surged most severely this summer. The new cases are not moving averages, so the charts are not quite comparable to those above. However, the peaks seem to occur prior to the breach of the 15% infection level.

Speculation about early herd immunity has been going on for several months with respect to various countries and even more “micro” settings such as cruise ships and military vessels, where populations are completely isolated. Early on, this “early” herd immunity was discussed under the aegis of “immunological dark matter”, but we know now that T-cell immunity has played an important role. In any case, anti-body expression (or seroprevalence) at around 20% has been linked to reversals in C19 cases and deaths in several countries. As Yinon Weiss notes, New York City and Stockholm were both C19 hotspots in the spring, both have seen deaths decline to low levels, and they have little in common in terms of public health policy. London as well. The one thing they share are similar levels of seroprevalence.

An important qualification is that herd immunity is not relevant at high levels of aggregation. That is, herd immunity won’t be achieved simultaneously in all regions. The New York City metro area might have reached its HIT in April, but Florida (or perhaps only Miami) might have reached a HIT in July. Many areas of the Midwest probably still aren’t there.

In the absence of a new mutation of C19, the final proof of herd immunity in many of the former hotspots will be in the fall and winter. We should expect at least a few cases in those areas, but if there are more intense contagions, they should be confined to areas that have not yet seen a level of seroprevalence near 15%.