Hi,
Since the beginning of the pandemic you’ve been hearing about the reproduction number. That "R" stands for the average number of people one sick person infects.
The idea is that if that number rises above 1, the virus spreads exponentially – a development that doesn’t follow a linear trajectory, but instead grows ever faster.
If R is more or less equal to 1, the disease is "endemic", which means the number of new infections is fairly constant.
Many governments have set the goal to get the number below 1. On average, each infected person will then be replaced by less than 1 new infection. That way the virus would peter out.
The R has received a lot of PR in recent months. The reproduction number is in the newspapers, on national dashboards and I – among others – wrote an explainer about it.
But there is a problem: the R is only an average.
The Bill Gateses of the pandemic
As an old joke among statisticians goes: when Bill Gates gets on a bus, every passenger becomes a millionaire on average. If you want to understand more about the wealth of the people on the bus, that average is pretty useless.
The reproduction number is also an average. But what if there are Bill Gateses among the infected? In other words, what if there are people who infect a lot more people than others? These are the so-called "super-spreaders".
Take the first Sars patient in Singapore. On 1 March 2003, 23-year-old Esther Sally Mok ended up in Tan Tock Seng Hospital in Singapore. A few days earlier, she had returned from a trip to Hong Kong and wasn’t feeling well.
On 25 March, her father died. A day later, her pastor died. Her mother would also die. In total, Mok infected at least 24 people.
If 35 people do not infect anyone but one person infects 24, as Mok did, then the R is below 1 (24 infections divided by 36 people equals 2/3).
As you can see: the R may be below 1, but there may still be an outbreak to worry about. And that’s the case with the coronavirus.
K
It is now clear that super-spreaders play an important role in the spread of the virus – it is even estimated that only 10 to 20% of those infected are responsible for 80% of infections.
Actually, it’s better to speak of "super-spreading events". Because these are often outbreaks that occur in certain situations, such as in nursing homes, prisons, nightclubs and on cruise ships. Places, therefore, that meet the three c’s: closed spaces, crowded places and close-contact settings.
Such super-spreading events influence how the virus then spreads. And so you want to prevent them or, at the very least, quickly detect them. If you get hold of the smouldering cigarette, you can prevent a forest fire.
But in order to understand super-spreading events, the R is not as informative. Because there is a sizeable group of people who don’t infect anyone at all. And then you have the Bill Gateses.
That’s why researchers also look, besides the R, at the K – the degree of dispersion. Where R is about the average, K is about the variation around that average. The formula is a bit complicated, but Adam Kucharski explained a rule of thumb to The Guardian.
(Kucharski is affiliated with the London School of Hygiene and Tropical Medicine and author of the book The Rules of Contagion.)
“The general rule is that the smaller the K value is, the more transmission comes from a smaller number of infectious people [ ... ]”, he said. "Once K is below one, you have got the potential for super-spreading.”
Consequences for policy
Super-spreading has important consequences for testing and source and contact research. Zeynep Tufekci explained that last week in a great piece for The Atlantic.
For example, contact tracing often looks at who an infected person was in contact with after the infection, to warn those people and to make sure that they go into quarantine.
But maybe it is more useful, explains Tufekci, when you look backwards. To the source of the infection. Probably someone has been infected by someone who in turn has infected a lot of people.
She refers to the "friendship paradox": it is very likely that your friends, on average, have more friends than you. (I feel a little better since knowing about that paradox ... )
It is the same with corona infections. On average, you will be infected by someone who infects more people than you will. (Are you still following? Tufekci explains it in more detail).
Once you’ve found the source, you can look ahead from there. And you will probably find a lot more people infected with this backward tracing method than with forward tracing.
The entire article by Tufekci is a must-read: she also elaborates on "cluster busting" – a wonderful term that a colleague immediately associated with the Ghostbusters.
More generally, following Tufekci is highly recommended; she has been doing very interesting work since the beginning of the pandemic (and before that as well). If you want to know more about her, read the profile in The New York Times.
Long-haulers
Last week I talked about "long-haulers", people who continue to suffer from symptoms long after a corona infection. I got a lot of replies, many thanks!
In the meantime I’m talking to quite a few people. Do you have any reading tips or questions? Do you know doctors or researchers who deal with "long covid" in their work? I would love to hear from you.
Before you go ...
Last week I published a review on Strangers in Their Own Land, in which sociologist Arlie Hochschild talks to archconservative Americans. A good example of how you can immerse yourself in people who think differently from you. As a Correspondent member said in the contributions: Hochschild for president!
A number of paragraphs in this newsletter come from my explainer about the reproduction number.
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