Super spreader immunity vs. herd immunity, from Paul Seabright

Dear Tyler,

I’ve read the comments section of your post on herd immunity pretty carefully and a point nobody has yet brought out is the importance of variance in R0. Suppose that an average R0 of 2.72 is made up of a) a low spreader subset of 90% of the population with R0 of 0.8 and b) 10% of super spreaders with an R0 of 20.

If what makes super spreaders different from the rest is just some invisible genetic factor, then using the average R0 of 2.72 in simulations may be a good approximation, and relaxing social distancing after the first wave may indeed lead to a large second wave.

But if what makes super spreaders different is a behavioral characteristic that also makes them much more likely to be infected than the rest of the population during the first wave, then the effect of the first wave may be much more permanent than the average R0 of 2.72 can capture.

Suppose the first wave infects 5% of low spreaders and 50% of high spreaders. Then after the first wave the uninfected population consists of a much smaller proportion of super spreaders than before and R0 for that population drops dramatically (to 1.86 in this example).

More generally if there is variance in systematic individual characteristics that affect R0 (and not just chance factors particular to the first wave), then stopping the epidemic requires only that enough of the high R0 individuals acquire immunity. That may happen naturally in the first wave, or it might be something that policy could influence. We may soon be able to test this by looking for a second wave in China as restrictions are relaxed.

An even more general point is that, unlike in many other familiar contexts, inequality in R0 is really good news. It reduces the size of the set of individuals whose behavior you need to influence. The more inequality the better!

Comments

Not a bad bit of thinking, but I doubt there is a lot of consistency between super spreaders over time. I'm not very sociable but I can become a super spreader after straining by back and taking pain killers that mask my symptoms a couple of days before I have to take a flight.

On the other hand, there is likely to be some consistency and so, hopefully, subsequent outbreaks won't spread as fast.

I found the point of the OP a bit confusing, and the reasoning that super-spreaders have social behavior different than non-spreaders speculative. Nevertheless the anonymous author is right, in that 'herd immunity' of the Dr. Robin Hanson / B. Cole / Dr. Ferguson (UK) variety may indeed be the solution, as I too have reluctantly endorsed (I hope I'm wrong, though as I said before due to my money I am betting I'm in the 40% that doesn't get infected with Covid-19 but nevertheless enjoys the herd immunity conferred by the infected 60%; sorry 99%-ers but you have to take a magic bullet for the 1%).

Note the author understands the point I've been harping upon now for over a month: it's the NEW cases IN CHINA that matter. The only thing that matters, as CHN has been time-wise in the vanguard. Not Singapore, not South Korea, certainly not Italy. New cases in China. Only. And today, once again, as Chinese 'go back to work after the quarantine', the new cases are edging back up. Uh-oh.

I'll just mention if you are going to use the term "herd immunity" it's probably best to point out any assumptions being used. For example:

1. Does infection with COVID-19 confer immunity? If so, in how many people and for how long?

2. What are the chances of this immunity working against new strains that may crop up?

3. Are wild cards ruled out such as it being one of those rare diseases where the second exposure is worse?

4. Is it assumed that survivors can't be carriers?

5. etc.

It might even be best not to use the term at all.

China seems to have had some success treating patients with serum from recovered patients. That implies that survivors have at least limited immunity for a limited time.

The SEIR model is oversimplified in that it doesn't live on a network. From a network perspective, what things probably look a bit more like is this: we have clusters of people who are either mostly infected or mostly uninfected and little between (and significant variability in the number of edges at each node). The focus of social distancing is most effective when it decreases spread along weak times of the network, which is where you really see propagation.

My armchair speculation is that it is totally plausible for infection to spread almost as powerfully along these unexposed cliques during the second wave.

It's a graph. Vertices = people. Edges = opportunities to spread a virus.

Highly connected people get infected early. As those people get infected, it speeds up (faster than exponential at first) but then it spreads to less connected people and the percentage growth slows (r0 drops). Plus connected edges are already infected so it slows down more.

Also "flattening the curve" doesn't just spread the healthcare need over time, it reduces the number of infections. The viruses misses opportunities to take a path to a person and that path closes off as the person becomes immune.

That last part should have said the path closes because vertices along the path are immune.

"Also "flattening the curve" doesn't just spread the healthcare need over time, it reduces the number of infections."

In the short-run, yes. But over longer periods of time, people move, travel, interact with new people, and the previously unexposed will ultimately always be at risk without a vaccine or mutation of the virus that renders it harmless. Measles and chickenpox didn't disappear on their own. Rather, communities experienced period outbreaks triggered by population shifts or changing hygiene habits.

Sounds like AIDS. Can't catch AIDS through sneezing [as far as I know].

You certainly shouldn’t sneeze while having intercourse with a gay man with AIDS. That’s nothing to sneeze at, but it’s not the sneezing that infects you!

Apologies for incorrect analogy. AIDS doesn't self cure.

So far, it looks like it's being spread most by the vigorous, normally healthy, and popular: skiers, movie stars, politicians, etc. For example, the Prince of Monaco, the son of Grace Kelly, has it. His winter had so far been full of ski-related charity events for jet-setters.

Excellent!

So, stay away from the popular people!

I suspect handshaking is a sizable pathway.

If you were going to make up a list of individuals in this world who the highest percentage of their fellow humans would like to be able to tell their friends: "Do you know whose hand I shook today?" Tom Hanks would likely be in the top 100.

That's a good point. Also, churches and mosques seem to be major hotspots. Singapore traced one outbreak to a dinner party and many of the other cases seem to come from religious services, international travel and live-in maids contracting it from their household employers.

I agree that inequality in Ro due to behavior is a good thing and perhaps a bad thing.
1- bad thing: before infection is noticed and tracking and quarantine become prevalent: the silent epidemic grows perhaps too large to be subsequently contained( Italy)
2- good thing. Quarantine shuts the super spreaders down and tracking makes them noticeable quickly
regarding 1- it's still possible super spreaders become the canary in the coal mine. Many cases occur simultaneously ( like the Korean sect) and just cannot go unnoticed. Health authorities realize quickly an epidemic is starting( Korea)

The more I read about herd immunity the more the idea is USELESS WITHOUT A VACCINE. Otherwise, nobody will go along with your idea because nobody wants to play Russian roulette. I'd like to believe that this is just another "too clever" autistic savant using more "too clever" arguments but I'm now suspecting an agenda here.

Vaccines take a long time. 18 months to deployment would be quicker than basically any other disease afaik.

If the choice is herd immunity or 18 months of near lockdown, lots of people would want to play this Russian roulette.

The US spent 58,000 lives and around $1 trillion in today's money to keep South Vietnam Thiệu. But when it comes to keeping 1,000,000+ Americans citizens alive you don' think they could be bothered?

18 months of virtual imprisonment plus an economic cost far in excess of $1 trillion in that short period would be a very tall order indeed. Color me skeptical.

My point is the United States will go to great lengths to fight enemies that pose no serious threat to them. So I doubt it's in their national character to just roll over and surrender when faced with an enemy that has already killed on American soil and has the potential to kill millions of US citizens.

Sure, they may give up after the cost of fighting is shown to be not worth it, but it can take them years or decades to reach that point.

"If the choice is herd immunity or 18 months of near lockdown, lots of people would want to play this Russian roulette."

Good thing your dichotomy as presented doesn't exist in real life. There was no herd immunity for SARS-CoV and you assume there's herd immunity for SARS-CoV-2 when there's absolutely no evidence. Hubei is coming out of lockdown, definitely not 18 months.

I’m not sure super spreaders are much more likely to infected. My suspicion is they’re people who get infected but have only mild symptoms (perhaps despite a high virus load in their mucous) and so go to work, go shopping, hit the town etc. and that’s how they ‘super spread.’

What’s wrong with “going shopping”? I mean for food and other essentials and near essentials.

You would think that right now, superspreaders would be those people who both have mild symptoms, and also come into close contact with lots of other people due to some behavioral/sociological quirk of not being concerned with potentially infecting others. So they shouldn’t be random throughout the population. My expectation is that a lot more people belonging to small, cultish religious groups and people with dark triad personality traits are likelier to both get and spread the virus.

Interesting point.

This is the kind of nonsensical speculation that adds nothing but noise. It's clear that the default R0 (the spread rate with no measures in place) for the majority of people is > 1. There's no need to imagine a what-if scenario where 90% (!) of people have an R0 of < 1 in the naive situation.

Of the many thousands of cases in this pandemic is there evidence of superspreaders? There are reported cases of a single person infecting up to 5 others. Hmmm, not exactly super. Now I'm seeing discussions of "super-spreading episodes" (i.e., an event where a bunch of people interact and share germs, aka "normal life at tourist attractions and business conferences).

We already know that young people are much less symptomatic, are capable of spreading the virus, are prone to feeling invulnerable, are prone to being thoughtless, and are highly social. The young idiot who lives above me had a party last night at a time when most responsible
adults are practicing social distancing. The fact that young people and children rarely get seriously ill makes them the likely super spreaders. Or perhaps the better term would be "stealth spreaders."

So will things get better after they (the young stealth spreaders and the older kinda-slightly-almost-super-spreaders) have all been sick and have immunity? Well, first let's figure out how strong the long-term immunity is first. Hopefully its strong and permanent.

Then lets digest the fact that even if 10 times as many people are now infected than we've documented, we aren't even close to a 1% infection rate in China or Italy. So we've only got about 59-79% of the population left to infect to possibly start talking about herd immunity.

+1. It has too many low probability assumptions. No evidence for herd immunity. No details for how authorities will identify super spreaders. Assumes that super spreader population does not change over time. Assumes a vaccine can be found before first or second wave. Assumes that there is a vaccine.

I safely put this in the "ignore" column until new evidence pops up.

Also we've already had a substantial number of cases carefully tracked to their contacts. It's true that most cases are not having their contacts tested, but there are hundreds of exhaustively documented examples where a single infected person and all their close contacts have been tracked and tested. If there were genuine super spreaders we'd have an idea about that already. A few countries are doing a good job with this tracking and isolating, and they are not seeing anything like this theoretical cohort of individuals with extremely high R0.

What about that women and the cult in South Korea?

So did Lombardy and Hubei achieve herd immunity? Everybody there got exposed and the ones that survived probably have some kind of immunity. According to this theory, there shouldn't even be a second wave in those places since everybody got it the first around.

Testing this in China will be possible only after first wave is over - it was contained in Wuhan - so all the superspreaders outside are yet to get immunised. In the data there were some who infected 1000 people- maybe AI can be trained to match such persons and applied on databases in other regions to identify and take measures.

The other side of things also matters. In any given population there are people who are simply easier to infect. The elderly, the immunocompromised, the MSM population, weird cults with odd rituals. We would expect rapid transmission in some or all of these groups during an initial wave because they have biological or social factors that encourage transmission.

For instance, Shincheonji appears to have had one super spreader, but the rituals of the religion (e.g. close, prolonged contact at mandatory religious services) make it a target rich environment. Any second wave will not have this pool of easily infected folks due to hopefully either immune resistance or social changes in rituals.

And it is like this for many other illnesses. Local flu numbers, for instance, spike massively when it hits nursing homes but as the high volume targets go down, further spread is slower.

While not always true, in general the most target rich parts of the infectious network fall first. Somebody might a superspreader in wave one just by being the entry point to this target rich environment. In wave two they might actually have below average spread.

If that enough of an issue to make the whole problem much safer, I don't think you would see the same level of double bounces in the numbers from the Spanish flu outbreak

"But if what makes super spreaders different is a behavioral characteristic that also makes them much more likely to be infected than the rest of the population during the first wave..."

Is there anything to suggest this might be the case? I can't think of any reason.

"stopping the epidemic requires only that enough of the high R0 individuals acquire immunity. That may happen naturally in the first wave, or it might be something that policy could influence."

Well, we could kill 'em.

The so-called patient 1 in Lombardy, Italy, fits the description of a behavioral super spreader. In a relatively short span of a week or so he had managed to do an inordinate number of things, ranging from work meetings, to social dinners, to team sports, thus infecting a large number of people. He is a 38 year old who just recovered

Given the importance of superspreader events, I've compiled a list of major ones in several countries in this google doc. It is open for others to carefully contribute
https://docs.google.com/document/d/19jKagFDrhD8sfqt8XSWRuNvWftuP5aDeDuzVaKGYArI/edit?usp=drivesdk

Taleb warned about the variance of R0 from the beginning. Even recommended that journalists shouldnt use it because of the variance.

https://arxiv.org/pdf/cond-mat/0107420.pdf

A version of this point has been made more quantitatively back in 2002. Whether it's an accurate model is a more subtle question.

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