The variation in the R rate between infected individuals

From Apollo’s Arrow: The Profound and Enduring Impact of Coronavirus on the Way We Live by Nicholas Christakis, pg 52. I found this really useful for getting my head around how outbreaks are dispersed as a consequence of physiological, behavioural and social differences between people who are infected:

This variation in R0 across individuals in a population can be quantified, and this quantity can have subtle but important effects on the course of an epidemic. The higher this variation (or dispersion), the more likely an epidemic will feature both super-spreading events and dead-end transmission chains. That is, an epidemic involving a population of people for whom the R0 is a steady 3 for every person can have a very different course than an epidemic involving a population for whom the R0 ranges from 0 to 10, even if the average R0 is still 3. If this variation in R0 is large, the risk of an outbreak starting from any given person falls substantially because there will be many more people who cannot spread the germ than people who can.

On pg 53 he explains the difference between SARS-1 and the novel coronavirus in these terms. The variation matters because it suggests we are all at risk of transmitting coronavirus (though in some cases as super spreaders) rather than a more bifurcated pattern of transmission dead-ends in most cases with superspreaders accounting for most or all of the onward transmission:

An epidemic with large variation in individual R0 manifests itself with many super-spreaders and super-spreading events. This is what happened with SARS-1.42 For SARS-1, it was estimated that four importations were necessary for one transmission chain to be initiated (the other three importations would fail to start epidemics and die out). However, when an outbreak did occur, it was likely to be explosive. For SARS-2, it looks like the variation in R0 is somewhat lower than for SARS-1, so while super-spreading events do occur, they are less common than the more frequent, humdrum chains of transmission.

His description of the role network structure plays in shaping these dynamics is illuminating. Popular people have more connections, which tends to entail more interactions, meaning they have a higher propensity for transmission. But they also tend to be infected earlier in a pandemic for the same reasons, meaning their network centrality ceases to function as a vector of transmission. This has implications for herd immunity as he describes it on pg 56:

The concept is that, if a sufficiently large number of people have acquired immunity to a disease (either by getting it and surviving or by being vaccinated), then any individual in this population who somehow contracts the illness is unlikely to encounter another person to whom he or she can transmit it. Hence, even if the chain of transmission somehow got started, it would die out.

This means that less infectious diseases require less of the population to be vaccinated in order to achieve herd immunity. If the novel coronavirus has a R0 of 3 (as has been estimated) then it would mean that 67% of the population would need to be vaccinated. However Christakis suggests this formal calculation is an overestimate when you consider variations in network structure as described above i.e. not everyone has an equal chance of interacting with every other person in the population.

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