I am grateful to Fergus Hamilton for drawing an important paper in Nature to my attention.[1] This paper compares models of the spread of an epidemic according to assumptions about the variance in infectivity from one infected person to another. R₀ represents the mean infectivity of an infected person, but some infected people seldom spread the disease, while others are super spreaders.

In this paper, a model, which assumes a symmetrical distribution of infectivity around the mean, is compared with more realistic models, which are heavily right skewed towards super spreaders.

The skewed models, when compared with symmetrical models, predict much more rapid spread and shorter lasting epidemics.

Data for the COVID-19 pandemic are not yet available. However, the degree of skewness is available for many other diseases. For example plague is not very skewed; the proportion of transmissions due to the most infectious cases is relatively low. On the other hand, measles and SARS are more skewed, and over 80% of transmissions are caused by just 20% of infected people.

Heterogeneity of infectiousness can explain why only about 20% of spouses catch the disease when living with an infected partner. One hopeful corollary is that a disease can be extinguished when R₀ is greater than one, if infectiousness is highly variable across the population. That said, quarantine can increase heterogeneity, favoring extinction but risking further sporadic outbreaks.

Richard Lilford, ARC WM Director

Reference:

1. Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease emergence. Nature. 2005; 438: 355–9.