Gomes

Article

Note on "Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold" by M. Gabriella M. Gomes et al.

Summary

This paper made a media splash early in May 2020 with headlines such as "Herd immunity may only need 10-20 per cent of people to be infected".

My opinion:

• There is likely to be an effect: a reduced herd immunity threshold (HIT) due to people being differently susceptible/infectious compared with what simple homogeneous modelling would suggest.
• This is a valuable point to make given that many people seem to be taking as read that the herd immunity threshold must be 60-70%, and we obviously very much need to know when herd immunity arises and to what extent we are feeling its effects now. However,
• I doubt that a HIT as low as 10-20% is likely. It arises in this paper's model from an extreme distribution of susceptibilities where there is a big concentration at the low end.
• Contrary to the practice in the paper, I believe the Coefficient of Variation (CV) is not a suitable parameter to use to measure how much the susceptibility distribution varies from a point value (constant): by choice of distribution you can get a huge variation in HIT for a given CV. That makes it dangerous to use, as the authors do at one point, an empirical/measured CV from one setting and translate it into a CV of a particular distribution (Gamma) in their idealised setting. Furthermore, there is a straightforward way to evaluate the HIT directly from the distribution (which the authors don't appear to have considered) so there is no need for proxy indicators like CV.
• There is a question of to what extent inhomogeneity in susceptibility is already taken into account in existing modelling - is it taken into account enough? I don't know the answer to this, and probably other people would be better placed to comment. Of course epidemiologists use mixing matrices based on age, location and other things which will certainly account for some of the inhomogeneity: for example Prem et al and Klepac et al. But it is conceivable (from the point of view of my limited knowledge) that these efforts, which are based on empirical data, don't go far enough because it's hard to take into account all of the "assortative" behaviours people engage in. (For example - illustrative, not a real example - if your mixing matrix classifies people into football supporters or not, that would account for some inhomogeneity, but it may turn out that you really need to take account of what particular team people support, because supporters tend very strongly only to mix with those of the same team.) If that is true, then there could be a case for artificially boosting inhomogeneity in the models (perhaps in the manner of Gomes et al) to account for the missing/unmeasurable inhomogeneity.