The pareto principle and stochasticity in COVID-19

Most of you know difference between parameters such as mean and standard deviation. Or, that distributions have variable dispersion or multi-modalities. Standard stuff.

In relation to COVID-19 it was clear early on that “superspreader events” were critical. That in fact, these events were driving the pandemic in some deep way, with there being huge variance in the number of people individuals have spread the disease to if they were infected.

Readers of this weblog will not be intimidated by a word like kurtosis. But it is different for readers of The Atlantic, notwithstanding the fact that they have the pleasure of imbibing the deep insights of America’s foremost public intellectual, Dr. Ibram X. Kendi. But rather than the august Dr. Kendi, I want to point you to Zeynep Tufekci, now at The Atlantic, but originally hired by The New York Times in March of 2015. Her piece, This Overlooked Variable Is the Key to the Pandemic, is probably what you should share with less statistically literate members of your family.

Tufekci’s piece is strewn with gems of fact. For example, ~70% of people infected with COVID-19 may not transmit it to anyone else, even if the mean number of transmissions is closer to 3 individuals. The explanation of what’s going on is that like many social science phenomena, but unlike influenza, the spreading of COVID-19 occurs through a minority of big transmitters. That is, it follows a power-law distribution and adheres to the Pareto principle.

Last spring I read that Japan was focused on super-spreader events, and was somewhat skeptical of this strategy. How could they identify superspreader events? Well, it turns out that these events tend to adhere to some necessary, though not sufficient, conditions. Large crowds, enclosed spaces, and poor ventilation. But, Tufekci also points out that superspreader events occur stochastically. Not all, or even most, instances, where conditions are met, will produce an outbreak. Some will. This is not surprising, but as she admits in the piece it’s a really difficult thing for people to accept and internalize. Sometimes we can’t always ascertain a specific cause. Stuff just happens.

Anyway, pass the piece on to your relatives and friends.


20 thoughts on “The pareto principle and stochasticity in COVID-19

  1. It’s sad what The Atlantic has become. It was huge in my cultural and literary development during high school and college. I remember avidly awaiting the annual fiction and poetry issue when they stopped inserting into the regular issues.

    Now, as you have lampshaded, it’s a joke, hackish even by the low standards of woke editorial boards, but still showing occasional glimpses of the august American journal of thought it once was, as this article shows.

    Depressing, really.

  2. Y’all can laugh at me but I think the Atlantic is one of the best Publications, especially their long-running series on the Constitution they have going right now. As long as you know which writers to avoid I think they still have really great stuff. And you can go in their archive and read stuff by Teddy Roosevelt and Henry David Thoreau, Frederick Douglass.

  3. Couldn’t it be that the genetic profile of a carrier could make the difference? I didnt look it up, but are there any papers about the virus burden different infected individuals produce? Its known from other viruses how different it can be based on the individual’s characteristics.
    If a “natural superspreader” meets the environment favourable for the distribution, it should be different from a low level “virus producer”.

  4. Thanks for this. It is the most important thing I have read, and explains a lot of what I have been seeing in Hong Kong.

    The biggest cluster that has happened in HK, called the “bar and band cluster” was caused by an infected singer with a live band that played in late night bars. She caused a cluster of 103 – bandmates, bar staff and patrons in several different bars that they played in.

    My gym has reopened, now that our third wave is over. Now I’m weighing the wisdom or otherwise of going back there again. It’s pretty well ventilated and rarely gets crowded; if it does, I always leave anyway, because trying to exercise with everyone sitting on the equipment reading their phones becomes impossible. Sometimes I tell them to get off so I can use it, but it gets tiresome.

    Someone needs to explain that to me some time – why people change into exercise attire, go to a gym and then just sit there on the equipment reading their phones, when they could more easily stay home and do the same thing.

  5. Actually singing and playing wind instruments is one of the more common scenarios for clusters, both churches, concerts and musical associations. Obviously, if a person which is a superspreader sings for half an hour or plays a trumpet, its even from the most basic understanding quite likely that the aerosols with viruses being spread throughout the space of a room, much more so than if sitting together in let’s say a cinema without too much talking and laughing.
    Same in public transport, there is a significant difference between sitting together with silent people or a couple talking with each other loudly throughout the whole ride. Just analyse what happens when people talk, even with most masks, they will simply eject more particles even from deep in their lungs, even worse when singing or playing a wind instrument – that’s like getting the content of their lungs directly in your face if they are close enough…

  6. @Robert Ford
    you can go in their archive and read stuff by Teddy Roosevelt and Henry David Thoreau, Frederick Douglass

    This makes Jeffrey Goldberg’s current reign seem even sadder.

  7. Japan seems to have done a much better job of limiting travel into the country from known hotspots. Would that we were allowed such.

    Another book along the lines those Razib linked with the article.
    The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow

  8. A lot of things in life – especially those that concern masses of people – are stochastic. That’s why “Hoping for the best and preparing for the worst” is often the best strategy for coping with the vagaries of life. Life is normal… until it isn’t suddenly.

    That’s also why conservatism is so natural. I think that was one of your points in recent posts.

    It’s also why I abhor the “just in time” distribution system. It’s hyper efficient, provided the environment is stable and predictable, but can be devastating in a sudden shock. Redundancy is expensive, but I see it as price worth paying as a form of insurance.

  9. Yesterday I linked an AP report of an article in Nature by Hugo Zeberg and Svante Paabo that identifies genes linked to a higher risk of hospitalization and respiratory failure in COVID-19 patients.

    Does anyone know of any broader GWAS studies on COVID-19 susceptibility or spreading?

    I think epidemiological models tend to treat individuals as identical black boxes. It is clear that age and sex affect suseptibility. Genetics would be another important factor.

    People who are concerned about their risk such as health care workers and teachers might be able to triage their risk and be transferred out of front line roles, or even be given disability retirement.

  10. @Twinkie, share the suspicion, although wonder how much agency we really will ultiamtely have in avoiding those failures of minimally redundant / heavily integrated systems.

    Like, on a different, but connected, topic, readers of this blog probably familiar by now with arguments by Walter Scheidel and Mark Koyama that having multiple political centres benefitted robusticity of European states in the long run, relative to China, which benefitted in the shorter term from forces pushing it towards higher levels of political unification and so higher economic growth and market integration. Any we could imagine people thinking about those as options and choosing one or the other.

    But in practice in most of these models, that wasn’t really a choice that either made – either “Fractured Land” and its consequences like linguistic divergence, or the threats from the steppe (or lack thereof), depending on the model, pushed each state system towards its form, despite aspirations to universal Christian empire in the Europe, or aspirations towards dynastic fracturing and local independence in China.

    So I wonder in the same way whether we will have any choice in how much our societies are pushed towards being “big”, globalized integrated societies with lots of fragile, non-redundant integration. Will any attempts to change course just end up marginalized by short term economic competitive forces?

  11. @worron – Heard any Cantonese speakers? People literally shout at each other, from like 2 feet away. Heard any Cantonese speakers inside crowded elevators? It’s deafening. And ventilation is generally poor, and people are crammed in uncomfortably close to each other. But everyone is wearing a mask. Hong Kong still has relatively low infection rate, even with the third wave which is now almost over. So I don’t buy it that loud speech is the sole factor, not at all.

    Carrying on from my comment above, I have been watching all of the Hong Kong cases closely, and I have seen not one case attributed to a gym, a yoga studio or some other enclosed indoor space devoted to groups of people exercising together. Particularly in weight training gyms, people are really breathing deeply and pumping out the exhaust air, often grunting loudly when they do. OK, stochasticity, but HK has a plethora of such places because the commercial rents are very high and the spaces are generally not large. But I guess they don’t get really too crowded, and the air exchanges from the air conditioning are pretty good, particularly in summer. Maybe more risky in winter when they recycle the air more and have fewer external air exchanges.

    Contrast with restaurants and bars, which have been implicated in multiple outbreaks. People take off their masks to eat, drink and shout at each other, and they really pack the customers in, or at least they did until the government forced distancing rules on them (which are frequently not complied with). Some outdoor food markets (wet markets) have been implicated (and where ventilation is not an issue), together with the usual suspects like meat packing plants and an abattoir. One Buddhist temple, which fits the template perfectly, ditto big weddings, crowded offices, shipping container terminals where all of the guys used the same crowded space to rest and change clothes, and a couple of construction sites ditto – if I had to choose one biggie, it would be restaurants. But outside of the “bar and band” cluster, the next two biggest were the container terminals and spreading among sales staff of a place like a pyramid selling organisation, where I guess the staff were crammed into inadequate and poorly ventilated office accomodation.

    I need to correct one thing I said, about the “bands and bars” cluster, having read the HK paper referenced in the Atlantic piece. I was going on media reports that the ‘index case’ was a singer, who had symptoms but went on working because she needed the money. The paper identifies the first two infected in that cluster as bar patrons and has been unable to identify how they became infected. If that’s right (and I’m not that convinced that it is, given the relative timing of the onset of symptoms), the media owe the singer an apology, but she won’t get one, particularly as she is likely to be a Filipina. The paper claims the whole cluster amounted to 106 cases, but the Centre for Health Protection (HK version of the CDC) say 103 cases. Depends how they are counting them, maybe. It’s a detail.

    The best single thing the government could do in preparation for a fourth wave would be to shut down all of the bars and restaurants, but they won’t, due to public and industry pressure.

    And get the university researchers working on what it is that makes people superspreaders, if they are not already – Obs’ suggestion seems like an obvious thing to look at.

  12. @Matt : But in practice in most of these models, that wasn’t really a choice that either made – either “Fractured Land” and its consequences like linguistic divergence, or the threats from the steppe (or lack thereof), depending on the model, pushed each state system towards its form, despite aspirations to universal Christian empire in the Europe, or aspirations towards dynastic fracturing and local independence in China.

    Don’t Cantonese and Mandarin differ from each other about as much as French and German? Until maybe the 17thC, the European solution to fractured languages (from, say, Poland on west) was much like that of China: a common tongue among the elite: in the one case, Mandarin, in the other, Latin. During the reign of Louis XIV, the universal language (of the elites) shifted to French, and finally in the early 20thC to English. I doubt that too many Chinese peasants spoke Mandarin before the 20thC (though I am ready to be corrected).

  13. @mp – Sure they did. Mandarin was the spoken language of the north and west. I’m not sure your comparison is valid, because China had a unified written language. In Empires of the Word (2005), Nicholas Ostler attributed the longevity of the Chinese civilisation to the written language as the glue that held the Empire together.

  14. @marcel, I think it’s a bit hard to compare divergence levels between different language families to be honest – or at least linguists never want to seem to do it (and I’d guess that to mean they don’t think it can be done well?). I think France and Germany are closer in distance than what I’d understand to be the core of Mandarin and Cantonese though (so if it’s a valid comparison it still seems a bit like more linguistic divergence over smaller spatial divergence?).

  15. Matt,

    You bring up a very good and interesting point. Yes, of course, there are structural constraints that may narrow the range of policy choices. In that regard, perhaps this novel Coronavirus pandemic may prove to have been a blessing in disguise. If nothing else, it taught many people to stockpile toilet paper (and other essentials of life). It certainly stress-tested our intensive care system, which turned out to be more robust and adaptable than previously feared. (By the way, the earlier MERS outbreak in South Korea likewise ended up helping the South Korean government to prepare more effectively for this pandemic.) Like the human body, governments and countries can also use “vaccines” of sorts every so often. 😉

    The thing is, no exogenous shock is truly completely unpredictable or impossible to prepare for. It’s just that too many political leaders (let alone the public) are self-indulgent these days and fail to recognize warning signs. During the Cold War, the leadership class in the U.S. was much more aware of existential threats (nuclear, biological, chemical warfare, etc.), considered them seriously, and prepared accordingly (e.g. I don’t live too far way from a deactivated “bunker” that was to serve as a shelter for the NCA in the event of an existential threat to the U.S.).

  16. @marcel I always thought French vs Spanish was a better analogy to Standard Mandarin vs Cantonese, in terms of linguistic distance and subjective similarity. French and Spanish are both descended from Vulgar Latin, much like how Standard Mandarin and Cantonese are both thought to be “descended” from Late Middle Chinese.

    Thanks for the article rec Razib!

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