Special K

"Superspreaders" is a name given to individuals infected with the novel coronavirus who pass it on to a very large number of their contacts. Many examples have been reported. For instance 29-year-old man infected 101 people after visiting several nightclubs in Seoul, South Korea; a singer unwittingly infected 52 fellow singers at a choir practice in Mount Vernon in Washington State in early March. Most of these multiple transmissions have taken place in crowded, poorly-ventilated places where the spreader was expelling plenty of virus-laden breath, say by singing or talking loudly over background noise. 

We have heard much about the statistical parameter R, called the epidemic reproduction number; it is the average number of contacts an infected person will pass the virus on to. For the coronavirus SARS-Cov-2 in a fully-susceptible population, the value of R lies between 2 and 3 in urban settings. As a proportion of the population becomes immune and social restrictions reduce the number of contacts, the value of R declines, and when it falls below 1, the epidemic will start to retreat. There is another parameter epidemiologists use called K. The value of K represents the level of individual variation in R. When K is small (less than 1), there will be wide variation in the number of people one infected person will infect; in particular, there will be more so-called superspreaders. In the early stages of the outbreak of covid-19 the value of K was between 0.1 and 0.5 which meant that 10-20% of those infected probably generated about 80% of the transmissions. An increase in the value of K, to above 5 say, will reflect the fact that the number of transmissions generated by most individuals will be close to the value of R.

Imagine a group of 200 individuals in a large population and divide them into  say 50 who are shielded and at no risk, and the other 150 who are moving out of lockdown as now. Assume that the number of active infections has significantly fallen and that the reproduction number is just below 1. Just as it was at the initial outbreak, the value of K will be small and the risk of the return of superspreaders high; it will only need one or two of them among the 150 to send the R-number soaring. This is why an effective test-and-trace system is so important at this stage, to catch the potential superspreaders before they have a chance to set off a second wave.