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@mgmgomes1 and coauthors have a preprint out where they analyze the impact of models incorporating variability in exposure (contacts) or susceptibility on epidemic trajectories in several countries. Quick thread on this and recent reaction to it. 
1/17
https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v1.full.pdf
1/17https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v1.full.pdf
@joel_c_miller has an analysis of this paper making the rounds ( @CT_Bergstrom, @akcayerol, etc). I certainly agree with some of his comments on the difficulty of this kind of work. But I disagree with his premise that the data already disagrees... 2/17 https://twitter.com/joel_c_miller/status/1286934179398131712
strongly with the predictions they've made.
In particular, I disagree that infection rates of over 20% in certain cities (NYC, Delhi) stand in contradiction with predictions of 10-20% HITs in the various countries they consider (Spain, England, Belgium, Portugal).
3/17
In particular, I disagree that infection rates of over 20% in certain cities (NYC, Delhi) stand in contradiction with predictions of 10-20% HITs in the various countries they consider (Spain, England, Belgium, Portugal).
3/17
To begin, let me clarify the minor point that, as far as I can tell, the HIT's predicted in this manuscript are not the same as the final epidemic sizes they predict in the real world under relaxing mitigations. As is well-known, HITs are overshot 
, 4/ https://twitter.com/CT_Bergstrom/status/1252075530276356101
, 4/ https://twitter.com/CT_Bergstrom/status/1252075530276356101
and by how much depends on how mitigations are implemented.
Now, more importantly, I think it is conceptually incorrect to compare attack rates in cities, particularly dense cities like Delhi and NYC (Manhattan is the densest city in the western hemisphere) to HITs... 5/17
Now, more importantly, I think it is conceptually incorrect to compare attack rates in cities, particularly dense cities like Delhi and NYC (Manhattan is the densest city in the western hemisphere) to HITs... 5/17
at the *country* level.
This is because R0 should be expected to be much higher in dense cities than in suburban or rural areas of a country. If the COVID epidemic ends with immunity in some country, then we should not expect that immunity to be uniformly distributed... 6/17
This is because R0 should be expected to be much higher in dense cities than in suburban or rural areas of a country. If the COVID epidemic ends with immunity in some country, then we should not expect that immunity to be uniformly distributed... 6/17
geographically; instead, it should be highest in dense cities, and lowest in rural areas.
In particular, in a hypothetical scenario where ~20% of the US became infected, we should expect that the infection rate would be significantly higher in dense cities than in rural areas.7/
In particular, in a hypothetical scenario where ~20% of the US became infected, we should expect that the infection rate would be significantly higher in dense cities than in rural areas.7/
(Of course, we should also expect exceptions to these general rules!)
What would the expected attack rate in NYC be in this scenario?
(drum roll...)
8/17
What would the expected attack rate in NYC be in this scenario?
(drum roll...)
8/17
I don't know (anyone?). Analyzing the relative contribution of regions of different densities to a country's overall epidemic seems like an interesting and important problem.
But I don't see a simple argument that it shouldn't be much more than the attack rate in the country..9/
But I don't see a simple argument that it shouldn't be much more than the attack rate in the country..9/
...overall.
All this is to say that as far as I can tell, there is no high quality data which seems in stark disagreement with what @mgmgomes1 and her co-authors are doing here.
Moreover: 10/
All this is to say that as far as I can tell, there is no high quality data which seems in stark disagreement with what @mgmgomes1 and her co-authors are doing here.
Moreover: 10/
Astonishingly, their work is the only serious work I am aware of which attempts to account for the effects of heterogeneity in an effort to actually predict the epidemic trends in specific countries.
So their analysis, right now at least, seems to be the only game in town. 11/
So their analysis, right now at least, seems to be the only game in town. 11/
That said, I agree with @joel_c_miller that there are some inherent difficulties in the problem they are tackling; in particular: understanding how people are actually interacting now, relative to how they were interacting before. They use google mobility data as a proxy... 12/
on behavior to justify their behavior model, but is that a good enough analog? Are there perhaps subtle things which are different now which are ignored by crude mobility data (how far apart people stand when they talk, etc)?
The flip side of this, however, is that... 13/
The flip side of this, however, is that... 13/
immunity doesn't only matter once some idealized threshold is reached and we can party like it's 2019 again.
It also matters if it makes a big difference in how sustainably an epidemic can be controlled with moderate measures. 14/
It also matters if it makes a big difference in how sustainably an epidemic can be controlled with moderate measures. 14/
One of the best things about this paper is that it was written.
Despite the obvious importance of understanding what lies ahead, the basic task of making some assumptions, incorporating known data, and then attempting to make realistic predictions of epidemic trajectories... 15/
Despite the obvious importance of understanding what lies ahead, the basic task of making some assumptions, incorporating known data, and then attempting to make realistic predictions of epidemic trajectories... 15/
under the influence of heterogeneity, in specific countries, seems not to have been carried out enough.
I think the best response to this paper now is for people to stick their neck out and make their own model of an epidemic under heterogeneity in an actual country. 16/
I think the best response to this paper now is for people to stick their neck out and make their own model of an epidemic under heterogeneity in an actual country. 16/
In particular, by making predictions about epidemic trajectories in the real world, using data from the countries they are actually studying, @mgmgomes1 and co-authors have given their predictions the weight of falsifiability.
17/17
17/17
