The “k” in COVID-19

Posted by Matt Birchler
— 2 min read

Ok, this Atlantic article is worth reading in full, but here are some highlights that give you a good summary.

By now many people have heard about R0—the basic reproductive number of a pathogen, a measure of its contagiousness on average. But unless you’ve been reading scientific journals, you’re less likely to have encountered k, the measure of its dispersion. The definition of k is a mouthful, but it’s simply a way of asking whether a virus spreads in a steady manner or in big bursts, whereby one person infects many, all at once. After nine months of collecting epidemiological data, we know that this is an overdispersed pathogen, meaning that it tends to spread in clusters, but this knowledge has not yet fully entered our way of thinking about the pandemic—or our preventive practices.


A recent paper found that in Hong Kong, which had extensive testing and contact tracing, about 19 percent of cases were responsible for 80 percent of transmission, while 69 percent of cases did not infect another person. This finding is not rare: Multiple studies from the beginning have suggested that as few as 10 to 20 percent of infected people may be responsible for as much as 80 to 90 percent of transmission, and that many people barely transmit it.

While incredibly variable, in a weird way it actually brings me some comfort to see the 80/20 apply here. It’s always 80/20, it seems.

This highly skewed, imbalanced distribution means that an early run of bad luck with a few super-spreading events, or clusters, can produce dramatically different outcomes even for otherwise similar countries.

This adds some context around the fact that seemingly similar locations taking very similar actions have had different results.

This kind of behavior, alternating between being super infectious and fairly noninfectious, is exactly what k captures, and what focusing solely on R hides.

Again, going back to the idea that the big number we’ve been focusing on is not the only measure that’s important, nor is it possibly the most important.

Oh, and they do mention every COVID-skeptic’s favorite, Sweden, and blasts holes through the talking points

From an overdispersion and super-spreading point of view, Sweden would not necessarily be classified as among the most lax countries, but nor is it the most strict. It simply doesn’t deserve this oversize place in our debates assessing different strategies.

So what’s the takeaway?

Could we get back to a much more normal life by focusing on limiting the conditions for super-spreading events, aggressively engaging in cluster-busting, and deploying cheap, rapid mass tests—that is, once we get our case numbers down to low enough numbers to carry out such a strategy? (Many places with low community transmission could start immediately.) Once we look for and see the forest, it becomes easier to find our way out.

That’s enough from me, and you should just go read it yourself, but it’s a really good look at how we should probably be shifting how we try and track this virus to be more effective in pinning it down and getting back to business as more-or-less “normal”.