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!
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: