Tag Archives: Reproduction Rate

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.

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.

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.

The Opportunity of Skewed Coronavirus Transmission

30 Monday Mar 2020

Posted by in economic growth, Pandemic

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People talk about the transmission rate or reproduction rate (R0) of Covid-19 as if it’s a single number that applies to the entire population. John Cochrane emphasizes the huge implications of this misperception for how best to prevent the spread of the virus, and at lower cost, and for how best to “restart” the economy.

First, however, lets dispense with the absolutist position that there can be no compromise on virus mitigation in favor of economic activity. I am not opposed to the “lockdown” we are now living, but it will have significant and unnecessary costs if it goes on too long: the lost output is a huge blow not only to our current lifestyles but to our ability to grow in the future, or even to afford better health care in the future. Beyond that, the lockdown has immediate negative impacts of its own on public health: economic stress leads to all kinds of terrible health outcomes like heart disease and even suicide. About the latter, the President is absolutely correct: if you need research to prove it, see here, here, here, and here, all respected journals (the links all courtesy of The Federalist.) Economic stress and isolation is quite likely to promote poor dietary habits, lethargy, and possibly family dysfunction as well. Don’t pretend there aren’t real tradeoffs between the economy, virus interventions, and public health. The trick is to improve those tradeoffs. A balance can and must be struck, and depending on policy actions, the tradeoff can be made better or worse.

Back to the virus reproduction rate: the R0 values we see quoted are estimates of the average number of other people infected by each infected person. A value of three means that each person infected with the virus passes it on to three others, on average. If R0 is greater than one, an epidemic grows. If R0 is less than one, a contagion recedes. It becomes a “non-epidemic” if R0 remains less than one. It does not have to be zero (and probably cannot be zero).

But not everyone is the same: my R0 is different from your R0 if only because we have different occupational exposure to others and different levels of social engagement. We also differ physiologically, which probably leads to differences in our “personal” R0 values. And an individual’s R0 will differ by time and place, depending on random circumstances like which way the wind is blowing. But here is where it gets interesting. Cochrane describes an extreme version of the skewed distribution shown at the top of this post:

“Suppose there are 100 people with a 0.5 reproduction rate, and 1 super-spreader with a 100 replication rate. The average reproduction rate is 1.5. Clearly, locking everyone down is wildly inefficient. It’s much more important to find the 1 super-spreader and lock him or her down, or change the business or behavior that’s causing the super-spreading.

This is exaggerated, but not far off the mark. I have not seen numbers on the distribution of reproduction rates across people, but it is a fair bet that it has an extremely fat tail. Most of us are washing our hands, social distancing, work in businesses that are shut down or are taking great steps to limit contact. And a few people and activities contribute to most of the spread.

This wide and fat-tailed dispersion is ignored in a lot of simulations I’ve seen. They take the average reproduction rate as the same for everyone. That’s a big mistake.

The danger: we waste a huge amount of time and money moving you and me from a 0.5 reproduction rate to an 0.4 reproduction rate. …  The opportunity: focus on the super-spreaders, and the super-spreading activities, and you bring down the reproduction rate at much lower cost. “

There are many ways to reduce R0. Cochrane gets a little more specific about this and the policy implications of the skewed R0 distribution across individuals:

“All we need is to get the transmission rate under one. Activities with possible but very low transmission rates, and high economic benefits should go on. Don’t separate to ‘essential’ and ‘non-essential.’ Separate into ‘high likelihood of transmission’ and ‘low likelihood of transmission.’

Why are we not using masks everywhere? Sure, they’re not perfect. Sure, an old hankerchief might only cut the chance of transmission by half. We’re not all surgeons. Cutting by half is enough to stop the virus. 

Conversely, why did they close the state parks? Really? Just how dangerous is it to drive the dog to a hiking trail and stay 6 feet away from other people? Parks, ski areas, golf courses, all sorts of businesses that surely can be run with a reproduction rate far less than one are just shut down. I met a realtor on our dog walk yesterday. They’re totally shut down. Just how hard is it to run a realty business with a 0.5 reproduction rate? One family in the house at a time, don’t touch anything, an hour between showings, stay 6 feet from the realtor… But instead the whole business is just shut down.”

The beginning of that last paragraph echoes a point I made in my last post about public park closures and the health benefits of getting outside generally.

Cochrane goes on to discuss several other policy options, including the potential benefits of simple kinds of testing and the overemphasis on false negatives and positives in policy discussions. Imperfect tests should not be discouraged by these concerns. If you’re worried about that, you shouldn’t use a thermometer either!

“Stay-at-home” or “shelter-in-place” orders will increasingly be tested by private parties if they remain in effect too long. That will be encouraged by the seemingly arbitrary distinctions some orders make between “essential” and “non-essential” activities. If workers or small businessmen judge themselves to be at low risk, they will take matters into their own hands to the extent they can. I believe that’s already happening where the specifics of “lockdown” orders have gone too far.  Workers at the low end of the income spectrum are especially hard hit by these orders. One can hardly blame them for trying to earn what they can if they believe, and their customers believe, their activities and interactions are of low risk.

Ultimately, the entire distribution of R0s will slide to the left. That will occur even at low levels of “herd immunity” and anything that offers at least weak prophylaxis. Broadly speaking, the latter includes maintaining distance, refusing admittance to venues with a fever, avoiding handshakes, wearing masks, and potentially chloroquine, which is already in widespread use by physicians treating coronavirus patients. Ultimately, a vaccine will slide the distribution far to the left, but the economy need not be held hostage until that time. To paraphrase Cochrane, we can get the transmission rate below one and keep it there without stopping the world permanently. There are many options, and now is the time for business and government to start planning for that.