Friday, August 07, 2020

Covid: The Invisible Elephant in the Room

Calculations of the requirement for herd immunity are based, as I understand it, on the implicit assumption that everyone is equally at risk, hence that the probability that one infected person will infect more than one other can be deduced from data on the early spread of the disease. That assumption is unlikely to be true, for both behavioral and biological reasons. Some people spend more time interacting at close range with those likely to be speaking loudly than others. And it seems likely that some can catch the disease more easily than others.

Suppose we drop that assumption. Suppose, for simplicity, that half the population consists of people vulnerable to the disease and half, for behavioral or biological reasons, invulnerable. Observing the early spread of the disease, we find that, on average, each infected person passes the disease on to two others. We conclude that we will only reach herd immunity when half the population have had the disease and become immune as a result.

But the relevant figure is not what fraction of the population has become immune but what fraction of the vulnerable population has. In my simple model, half the vulnerable population is only a quarter of the total population, so we reach herd immunity much earlier than the simple calculation implies. 

The real world distribution of vulnerability will, of course, be much more complicated than that, but the qualitative conclusion still holds. Over time, the people most vulnerable will be most likely to get the disease, so the average vulnerability of those who have not yet gotten it will decline, lowering the average number that each infected person passes the disease to. Hence herd immunity will come sooner than the simple calculation implies.

So far I have only considered differences in how easily individuals can get the disease. There will be similar differences, at least for behavioral reasons, to how easily individuals can transmit it. The two will tend to correlate — someone who spends a lot of time in loud conversation with lots of others will be more likely than average to get the disease and, if he gets it, more likely to pass it on. So, over time, the probability of transmission will fall as those most likely to transmit are selectively removed from the pool of potential transmitters.

All of this tells us that herd immunity will come earlier than the simple calculation implies, but not how much earlier — that depends on the actual distribution of vulnerability, of probability of transmission, and the correlation between the two.

Has anyone done the research necessary to estimate these numbers and recalculated the requirement for herd immunity according?

A further problem with the simple calculation is that it ignores behavioral changes due to the pandemic itself. Presumably part of the point of lockdowns was to temporarily push the transmission rate below one, driving the virus to near extinction — far enough down so that it could be controlled by a test and trace approach. In most countries that imposed a lockdown that didn't happen, but even without a lockdown the existence of the pandemic changes behavior in ways that should reduce the transmission rate below its initial value, at least somewhat.

P.S. a commenter on another blog where I raised the post gave two links to relevant material. The first goes to the editors' blog of Science magazine. The most interesting bit is:

we were concerned that forces that want to downplay the severity of the pandemic as well as the need for social distancing would seize on the results to suggest that the situation was less urgent. We decided that the benefit of providing the model to the scientific community was worthwhile.

That implies that the editors believe that part of their job is filtering the scientific literature in order to bias the public perception in the direction they approve of, although in this case they decided not to. It follows that one cannot take the published scientific literature on any controversial issue as giving an unbiased picture of the actual science. That is disturbing, but not surprising.

The post contains a link to the paper, which appears to be simply a fancier version of my argument, without actual empirical data that could be used to figure out the size of the effect.

The second link goes to a paper which, judged by the abstract, does make an attempt at estimating real world numbers, and concludes that particularly hard hit areas, such as New York City, may already be close to herd immunity. I couldn't find the full text online.

But a commenter could.


At 3:53 PM, August 07, 2020, Anonymous Anonymous said...

Link to full text of the second paper:

At 9:17 PM, August 07, 2020, Blogger Ricardo Cruz said...

It would be interesting to consider empirical studies in herd immunity. I remember hearing an epidemiologist saying these diseases have a hard time propagating after they have infected 20-30% of the population.

At 11:40 AM, August 08, 2020, Blogger Malcolm Kirkpatrick said...

The word "symptoms" names the disease reproductive strategy: coughing (influenza), salivating and biting (rabies), supperating sores (herpes), diarrhea (cholera), etc.
Symptomatic infection is a matter of degree. Exposed children get the Wuhan coronavirus and shrug it off. One quarter of infected people over age 80 die (apparently).

Moss Brennan, "For the second time, Virginia erroneously reports coronavirus death of a child", _The Virginian-Pilot_ (2020-Aug-07)
Virginia Department of Health Covid cases and deaths, by age
Cases and deaths:
80+: 4,508 cases, 1,144 deaths . Deaths/ cases ~ 0.2538
70-79: 4,799 cases, 582 deaths. Deaths/ cases ~ 0.1208
60-69: 9,237 cases, 355 deaths. Deaths/ cases ~ 0.0384
50-59: 14,158 cases, 145 deaths. Deaths/ cases ~ 0.0102
40-49: 16,222 cases, 62 deaths. Deaths/ cases ~ 0.0038
30-39: 17,954 cases, 20 deaths. Deaths/ cases ~ 0.0011
20-29: 18,869 cases, 6 deaths. Deaths/ cases ~ 0.0003
10-19: 7,693 cases, 0 deaths. Deaths/ cases ~ 0.00
0-9: 3,407 cases, 0 deaths. Deaths/ cases ~ 0.00

CDC, "Weekly Updates by Select Demographic and Geographic Characteristics"
See Table 1. "Deaths involving coronavirus disease 2019 (COVID-19), pneumonia, and influenza reported to NCHS by sex and age group. United States. Week ending 2/1/2020 to 7/25/2020"
According to CDC, the Wuhan coronavirus kills fewer adult human females than adult human males.
Female to male Covid-19 fatality ratio, by age
Age 0 to age 24: 98 to 172
Age 25 to age 64: 9,470 to 19,21
Age 65 to age 74: 11,349 to 18,520

Deoending on the degree to which exposure-induced immunity lasts (unknown, as yet), it looks like the sensible strategy is to minimize exposure of old people and to maximize exposure of children.

At 3:54 PM, August 08, 2020, Blogger Michael Wolf said...

Nobel Laureate Michael Levitt has been doing work on this since February, starting with the numbers out of China and the Diamond Princess cruise ship, and I believe had an early estimate of around (not exactly) 20% infected as the likely herd immunity threshold. You can follow him on twitter as well as easily google several articles and interviews with him over the past several months.

This has been borne out all over the place, as, based on seroprevalence data, the virus appears to burn out and slope downward somewhere in the 15-25% range. We see this clearly in Sweden, which never locked down. We also have seen it recently in Arizona, which resisted a second lockdown, and so was open (albeit with modifications and some restrictions) when the virus hit.

It appears there is cross immunity from previous exposure to other coronaviruses, as well as a large roll for T-cells here, that means we effectively hit the 60-80% threshold even when only 15-25% have antibodies.

Some links:
1. Estimate of 17% herd immunity threshold in Stockholm, the hardest hit part of Sweden:

2. Research from Sweden that offers an explanation why we are seeing burnout at much lower %s than the 60-80% herd immunity threshold initially speculated by many (and still used by many):

Also linked here to direct research.

3. Graph of Arizona, showing burnout starting to occur around the 15% seroprevalence mark:

There's a lot more out there about this, but going to Levitt, and these links, is a good start.

At 10:49 PM, August 09, 2020, Anonymous Anonymous said...

There is some discussion of these ideas here

At 4:43 PM, August 10, 2020, Anonymous RKN said...

That implies that the editors believe that part of their job is filtering the scientific literature in order to bias the public perception in the direction they approve of, although in this case they decided not to.

I don't think so.

There's a big difference between a cautionary remark about the possible misuse of a result, and censoring a result to bias a particular point of view. My reading of the
linked blog post classifies it as an example of the former, not one of an existential
crisis in the scientific literature.

At 7:44 PM, August 10, 2020, Blogger Michael Wolf said...

Another good twitter thread, with links, on the role of cross immunity with other coronaviruses and t cells large role in immunity, from which we see the ~20% herd immunity threshold looking a lot more realistic than the 60-80% number often still being used:

At 6:30 AM, August 11, 2020, Anonymous mister bitcoin said...

Michael Levitt, biophysicist at Stanford Medical and Nobel Prize winner in Chemistry.

Diamond Princess Cruise: 3711 passengers and crew, 20% infection rate, 1% case fatality rate, all deaths were people over age 70

He said this in March.

He correctly predicted Sweden will max out at 5000 deaths.

He predicts covid will dissipate on August 25 in US... number of excess deaths will hit zero

At 2:32 PM, August 12, 2020, Blogger David Friedman said...

@Mister Bitcoin:

Can you give me a cite for the Levitt prediction for the U.S.? I can't find it, and it doesn't sound plausible.

At 12:21 PM, August 15, 2020, Anonymous Mr Bitcoin said...

At 12:22 PM, August 15, 2020, Anonymous MR BITCOIN said...

I made a mistake about Sweden earlier.

I meant 6000 deaths, not 5000.

At 12:27 PM, August 15, 2020, Anonymous Mr Bitcoin said...

Michael Levitt predicts August 25

Sorry for making the previous links unclickable.

I thought blogger would do it automatically.

You can also click on my name to go to his twitter page

At 8:02 AM, August 18, 2020, Blogger Michael Wolf said...

Here's an update from Levitt with new CDC data for comparison. He quote-tweets his tweet from a few weeks ago where he said covid-19 will be epidemiologically over in the US by August 25th.

I don't see a hyperlink option but this should work as a copy & paste.

At 9:34 PM, August 24, 2020, Blogger Mr Bitcoin said...


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