I agree with your main claim that the protests will cause more deaths than they save, but I disagree with your estimate of caused deaths by at least an order of magnitude.′
The estimated change in reproduction number is not compelling. Firstly, the largest protest in American history had attendance of 3*10^6, or one in a hundred Americans. So assuming this protest is tied for most attended in US history, and other Americans behave the same, the protestors must each have an R of 30 to bring our average R from .9 to 1.25. That is 10 times the pre-SD reproduction number. Assuming the protestors have an R of 3 or 4 seems reasonable to me. Now that we know much transmission is from speaking, 10 would be the upper limit of my 95% CI. Assuming an R of the 3, reduce the estimate to 10%
Also the protests are short relative to the time a person is contagious. I doubt the protests will maintain attendance in the millions for more than two days, which is less than people are typically contagious. Therefore their influence on our effective reproduction number will be less than you estimate. Seems like people are contagious for at least 4 days, so call that a reduction by half. So reduce the estimate by a further 50%.
So I would reduce your estimate from 75,000 to 4,000. Which is still a lot. More than my expected benefit from the protests by movement building.
I am also sceptical about the central scenario. Protests have disproportionately high visibility relative to the numbers participating. If the 28% reduction Brauner et al estimate was the result of banning protests, parades, sporting events, concerts, political rallies, beach gatherings, lectures, house parties, crowded gyms and restaurants, yoga classes, and many other categories of >10 people gatherings, plus the indirect effects (e.g. on public transport etc) of these measures, then it seems unlikely to me that the recent protests could have an equivalent reverse impact, despite how relatively widespread they have been.
I think many of those examples would fall under their other categories like “Most Businesses Suspended” or “School Closure”. Things like ‘beach closures’ do not, but population density on beaches tends to be much lower than at protests (at least of the beaches I have been to).
Additionally, I worry that the protests might reduce other forms of social distancing. Imagine you are a moderate conservative, who had to cancel your son’s graduation and your daughter’s wedding, and hasn’t been able to go to confession for months. You wanted to go back to work, but all the experts told you that it was too dangerous, even though you knew you’d be careful. They even stopped you playing golf—you weren’t even allowed to do a couple of rounds by yourself, standing by yourself in the middle of the green! Now all of a sudden these so-called experts are joining the hippies in a chaotic screaming looting protest, with nary a six foot gap to be seen. How likely is it that you will trust them again?
I spent a while trying to estimate the r0 in this way, thinking about the dynamics of protests. In the end I couldn’t really come up with much confidence as any level of at-protest-r0; in particular it wasn’t obvious why it couldn’t be much higher, given the loud close contact between a very large number of people. It certainly seems plausible to me that an infected person could easily pass within one meter of a very large number of people. When I try to visualise the number of talking people I spent time close to pre-Covid, vs the number I would be close to at a busy protest, it doesn’t seem implausible to me that the latter could be orders of magnitude higher. But I don’t have any data on this so it is rather speculative!
This is an interesting point. The protests are happening largely outside so there is a further reduction, possibly itself an order of magnitude. So you really need two orders of magnitude to get one hundredth of Americans to contribute .3 to the reproduction number.
Imagine putting people into a room, and measuring the number of possible transmission paths. At one person in the room there are 0 possible transmissions. At two people, there is one possible transmission. 3 people, three transmissions. 4 people, 6 transmissions. The scaling is n! where n is the number of people in the room. So if protests involve a larger average number of people in breathing contact, then protesters might have an effective R ten times higher than our regular lives.
But that scaling only lasts out as far as the droplets spread. Do we model droplets as rays, equally likely to move in any direction? Then the droplet spread drops off by r^2 as the distance to another person. Then the connection factor stops scaling quickly because as people are packed in they become further away. I do not know when the n! scaling stops, but I imagine the number of protestors within 6 feet of one another is a good metric. The last protest I was at there were like 10 people within 6 feet of me. 10! is...
I was thinking about the outside issue. It seems in general this is quite protective, presumably because the wind blows the droplets away, rather than their being recycled in a largely air-tight room. But for a sufficiently large protest, presumably the wind is blowing them away… onto another part of the protest! So I worry that this factor will be less protective here.
Great explanation of the scaling issues, good way of thinking about it.
A protest near me had six foot markings on the ground to give each individual protester their own box… which was then ignored in practice.
Hey, thanks for this. Do you have any good data on the super-spreader events, and how to adjust for inside/outside? I agree that ‘you’ in a general sense can, but unfortunately this doesn’t mean that ‘I’ specifically can!
I agree with your main claim that the protests will cause more deaths than they save, but I disagree with your estimate of caused deaths by at least an order of magnitude.′
The estimated change in reproduction number is not compelling. Firstly, the largest protest in American history had attendance of 3*10^6, or one in a hundred Americans. So assuming this protest is tied for most attended in US history, and other Americans behave the same, the protestors must each have an R of 30 to bring our average R from .9 to 1.25. That is 10 times the pre-SD reproduction number. Assuming the protestors have an R of 3 or 4 seems reasonable to me. Now that we know much transmission is from speaking, 10 would be the upper limit of my 95% CI. Assuming an R of the 3, reduce the estimate to 10%
Also the protests are short relative to the time a person is contagious. I doubt the protests will maintain attendance in the millions for more than two days, which is less than people are typically contagious. Therefore their influence on our effective reproduction number will be less than you estimate. Seems like people are contagious for at least 4 days, so call that a reduction by half. So reduce the estimate by a further 50%.
So I would reduce your estimate from 75,000 to 4,000. Which is still a lot. More than my expected benefit from the protests by movement building.
I am also sceptical about the central scenario. Protests have disproportionately high visibility relative to the numbers participating. If the 28% reduction Brauner et al estimate was the result of banning protests, parades, sporting events, concerts, political rallies, beach gatherings, lectures, house parties, crowded gyms and restaurants, yoga classes, and many other categories of >10 people gatherings, plus the indirect effects (e.g. on public transport etc) of these measures, then it seems unlikely to me that the recent protests could have an equivalent reverse impact, despite how relatively widespread they have been.
I think many of those examples would fall under their other categories like “Most Businesses Suspended” or “School Closure”. Things like ‘beach closures’ do not, but population density on beaches tends to be much lower than at protests (at least of the beaches I have been to).
Additionally, I worry that the protests might reduce other forms of social distancing. Imagine you are a moderate conservative, who had to cancel your son’s graduation and your daughter’s wedding, and hasn’t been able to go to confession for months. You wanted to go back to work, but all the experts told you that it was too dangerous, even though you knew you’d be careful. They even stopped you playing golf—you weren’t even allowed to do a couple of rounds by yourself, standing by yourself in the middle of the green! Now all of a sudden these so-called experts are joining the hippies in a chaotic screaming looting protest, with nary a six foot gap to be seen. How likely is it that you will trust them again?
Thanks, good comment!
I spent a while trying to estimate the r0 in this way, thinking about the dynamics of protests. In the end I couldn’t really come up with much confidence as any level of at-protest-r0; in particular it wasn’t obvious why it couldn’t be much higher, given the loud close contact between a very large number of people. It certainly seems plausible to me that an infected person could easily pass within one meter of a very large number of people. When I try to visualise the number of talking people I spent time close to pre-Covid, vs the number I would be close to at a busy protest, it doesn’t seem implausible to me that the latter could be orders of magnitude higher. But I don’t have any data on this so it is rather speculative!
This is an interesting point. The protests are happening largely outside so there is a further reduction, possibly itself an order of magnitude. So you really need two orders of magnitude to get one hundredth of Americans to contribute .3 to the reproduction number.
Imagine putting people into a room, and measuring the number of possible transmission paths. At one person in the room there are 0 possible transmissions. At two people, there is one possible transmission. 3 people, three transmissions. 4 people, 6 transmissions. The scaling is n! where n is the number of people in the room. So if protests involve a larger average number of people in breathing contact, then protesters might have an effective R ten times higher than our regular lives.
But that scaling only lasts out as far as the droplets spread. Do we model droplets as rays, equally likely to move in any direction? Then the droplet spread drops off by r^2 as the distance to another person. Then the connection factor stops scaling quickly because as people are packed in they become further away. I do not know when the n! scaling stops, but I imagine the number of protestors within 6 feet of one another is a good metric. The last protest I was at there were like 10 people within 6 feet of me. 10! is...
Oh my. Perhaps the R0 jump will be noticable.
The number of possible pairs of people in a room of n people is about n^2/2, not n factorial. 10^2 is many orders of magnitude smaller than 10! :)
(I think you are making the mistake of multiplying together the contacts from each individual, rather than adding them together)
lol I thought that 10! was a surprise, rather than a factorial...
I was thinking about the outside issue. It seems in general this is quite protective, presumably because the wind blows the droplets away, rather than their being recycled in a largely air-tight room. But for a sufficiently large protest, presumably the wind is blowing them away… onto another part of the protest! So I worry that this factor will be less protective here.
Great explanation of the scaling issues, good way of thinking about it.
A protest near me had six foot markings on the ground to give each individual protester their own box… which was then ignored in practice.
Look at other superspreader events, like large church choirs. Those are indoors, so probably worse than protests, but you can adjust for that.
Hey, thanks for this. Do you have any good data on the super-spreader events, and how to adjust for inside/outside? I agree that ‘you’ in a general sense can, but unfortunately this doesn’t mean that ‘I’ specifically can!
Upvoted for this line, which made me laugh: