Pareto is always there

Back on April 7th, I speculated in Mystery vulnerability and super-spreaders about Covid-19 super spreaders.

See the original for the links.

The other phenomenon is the possible existence of rare super-spreaders. Examples from Georgia, Choir and Residential Care Facility.

In each of these instances, there is clearly the commonality of proximity and exposure. But, at least in the case of Georgia and with the choir, the exposure time is brief. In all three instances, there is an explosion of number of infections and number of deaths in a short time after the exposure at a greater speed, higher transmission and higher mortality than seems common elsewhere (for example the Diamond Princess cruise ship).

In the subsequent month and a half I occasionally see mention of super spreaders but no research, not data.

Until Why do some COVID-19 patients infect many others, whereas most don’t spread the virus at all? by Kai Kupferschmidt.

When 61 people met for a choir practice in a church in Mount Vernon, Washington, on 10 March, everything seemed normal. For 2.5 hours the chorists sang, snacked on cookies and oranges, and sang some more. But one of them had been suffering for 3 days from what felt like a cold—and turned out to be COVID-19. In the following weeks, 53 choir members got sick, three were hospitalized, and two died, according to a 12 May report by the U.S. Centers for Disease Control and Prevention (CDC) that meticulously reconstructed the tragedy.

Many similar “superspreading events” have occurred in the COVID-19 pandemic. A database by Gwenan Knight and colleagues at the London School of Hygiene & Tropical Medicine (LSHTM) lists an outbreak in a dormitory for migrant workers in Singapore linked to almost 800 cases; 80 infections tied to live music venues in Osaka, Japan; and a cluster of 65 cases resulting from Zumba classes in South Korea. Clusters have also occurred aboard ships and at nursing homes, meatpacking plants, ski resorts, churches, restaurants, hospitals, and prisons. Sometimes a single person infects dozens of people, whereas other clusters unfold across several generations of spread, in multiple venues.

Other infectious diseases also spread in clusters, and with close to 5 million reported COVID-19 cases worldwide, some big outbreaks were to be expected. But SARS-CoV-2, like two of its cousins, severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS), seems especially prone to attacking groups of tightly connected people while sparing others. It’s an encouraging finding, scientists say, because it suggests that restricting gatherings where superspreading is likely to occur will have a major impact on transmission, and that other restrictions—on outdoor activity, for example—might be eased.

“If you can predict what circumstances are giving rise to these events, the math shows you can really, very quickly curtail the ability of the disease to spread,” says Jamie Lloyd-Smith of the University of California, Los Angeles, who has studied the spread of many pathogens. But superspreading events are ill-understood and difficult to study, and the findings can lead to heartbreak and fear of stigma in patients who touch them off.

Most of the discussion around the spread of SARS-CoV-2 has concentrated on the average number of new infections caused by each patient. Without social distancing, this reproduction number (R) is about three. But in real life, some people infect many others and others don’t spread the disease at all. In fact, the latter is the norm, Lloyd-Smith says: “The consistent pattern is that the most common number is zero. Most people do not transmit.”

That’s why in addition to R, scientists use a value called the dispersion factor (k), which describes how much a disease clusters. The lower k is, the more transmission comes from a small number of people. In a seminal 2005 Nature paper, Lloyd-Smith and co-authors estimated that SARS—in which superspreading played a major role—had a k of 0.16. The estimated k for MERS, which emerged in 2012, is about 0.25. In the flu pandemic of 1918, in contrast, the value was about one, indicating that clusters played less of a role.

Estimates of k for SARS-CoV-2 vary. In January, Julien Riou and Christian Althaus at the University of Bern simulated the epidemic in China for different combinations of R and k and compared the outcomes with what had actually taken place. They concluded that k for COVID-19 is somewhat higher than for SARS and MERS. That seems about right, says Gabriel Leung, a modeler at the University of Hong Kong. “I don’t think this is quite like SARS or MERS, where we observed very large superspreading clusters,” Leung says. “But we are certainly seeing a lot of concentrated clusters where a small proportion of people are responsible for a large proportion of infections.” But in a recent preprint, Adam Kucharski of LSHTM estimated that k for COVID-19 is as low as 0.1. “Probably about 10% of cases lead to 80% of the spread,” Kucharski says.

That could explain some puzzling aspects of this pandemic, including why the virus did not take off around the world sooner after it emerged in China, and why some very early cases elsewhere—such as one in France in late December 2019, reported on 3 May—apparently failed to ignite a wider outbreak. If k is really 0.1, then most chains of infection die out by themselves and SARS-CoV-2 needs to be introduced undetected into a new country at least four times to have an even chance of establishing itself, Kucharski says. If the Chinese epidemic was a big fire that sent sparks flying around the world, most of the sparks simply fizzled out.

Read the whole thing. Interesting throughout.

The article mirrors some of the speculative hypotheses I mentioned and provides some new data. Research is underway but nothing definitive yet. This was new to me:

Individual patients’ characteristics play a role as well. Some people shed far more virus, and for a longer period of time, than others, perhaps because of differences in their immune system or the distribution of virus receptors in their body. A 2019 study of healthy people showed some breathe out many more particles than others when they talk.

I knew there was variation in viral load but not that it might materially impact transmission probability.

Interesting, though not unexpected, to see the Pareto distribution of cases.

“Probably about 10% of cases lead to 80% of the spread”

There has been a lot of commentary about testing as a predicate to track-and-trace. The challenge of track-and-trace is that we are a huge nation geographically and in terms of headcount. It is difficult to track people.

All the articles which I have read treat track-and-trace as uniform process. But if there are superspreaders who can be identified who are responsible for 80% of transmission, that suggests the capacity to become much more targeted and makes track-and-trace a much more viable strategy. If.

Seems like the story of Covid-19 is the story of blanket plausible solutions in the face of near-complete incomprehension followed by an awareness of the inadequacy and cost of one size-fits-all solutions, followed by a slow refining and targeting of solutions.

Good that we are making progress. Bad that it has taken so long. Terrible that the very institutions who were tasked with being prepared (WHO, CDC, FDA) were so completely unprepared.

Kind of heartening that the wisdom of crowds can be such a bulwark in the face of misguided authority, nominal expertise, and the rank idolatry of credentialism.