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A new paper is out exploring the impact of heterogeneity on the herd immunity threshold.

It explores two types of heterogeneity
- variation in susceptibility
- and variation in contact rate.…
It reaches a surprisingly low value (~10%!!) for the potential herd immunity threshold under infection-acquired immunity.

The reason that infection-acquired immunity is highly effective when these heterogeneities exist is that infection acts like a targeted vaccine.
The people who are most likely to get infected early on (and thus play the largest role in onwards transmission) get infected in the first pass of the epidemic.
If you can keep infection rates down and then suppress the epidemic, the residual population is largely spared infection, but largely consists of people who do not spread the disease well.
So the effect is real. But I doubt it is as large as this study suggests.

I am dubious about the assumptions made about heterogeneity, and I think the techniques used to measure it will struggle to disentangle the effects from interventions or behavior change.
All that said, Gabriela Gomes is an excellent researcher, so I don't think we can discount it out of hand.

What I'm giving here is my first impression, on Saturday, while trying to spend time with my kids. So grains of salt are needed, and others should look closely.
First - why would I find such low values very surprising?

Along with the low herd immunity thresholds, these models would predict low levels of infection, even in unmitigated epidemics.
Iquitos, Peru appears to have had 70% infected.

This is inconsistent with such high levels of heterogeneity in population structure.

The model only predicts such high attack rates if we assume the heterogeneity is low.
Both New York and New Delhi have had over 20% infected, with significant interventions in place.

If these places had reached their herd immunity thresholds AND had effective interventions in place the disease should have just melted away.
These numbers seem to disagree with observations in at least some places.

So what do I think went wrong?
I think it is hard to measure a signature of heterogeneity from case reports:

Early in the epidemic, we saw exponential growth. Almost every model would predict this. At some point the epidemic deviates to a lower than exponential growth.
Before that deviation, there's an identifiability issue. If you've got more than one parameter in your model, there are probably infinitely many combinations that fit the observed growth.

So it's only after the deviation from exponential that you can start to fit parameters.
But, why did the epidemic deviate?

If we assume it's due to heterogeneity, then early deviation means higher heterogeneity.
This paper accounted for behavior change, but if I'm reading it correctly, it assumes the behavior started to change when policy changed.

I think people changed behavior sooner. If I'm right, I think this would cause their model to overestimate heterogeneity.
I've said before, I would not be surprised if the disease induced herd immunity threshold is around 40%, as opposed to the 60% or so a homogeneous model predicts. So the effect is real, but I don't think it's as big, and I don't think we should test it.
Unfortunately, I'm starting to think the US will answer this question for us.

Related work by myself and colleagues:

A Quanta magazine article on the topic (in which myself and Gabriela Gomes are interviewed):…
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