I wrote a simulation where some people are bigger spreaders than others (I used a geometric distribution), and I indeed found cases where 20 percent infected was enough to send R dropping to zero with no other interventions.
I had never thought that a number as low as 25 percent (say) would be enough, but your logic convinced me it was plausible, and the simulation confirmed it.
Zvi, what specific distribution were you thinking? I can find one where the top 20 percent makes up 80 percent of interactions, but if you have one in mind, I'll try that one in the sim and see what happens.
Oops! There was a problem with my simulation, where the random numbers were repeating. I fixed it, and the results changed. It now took about 45% infected before R dropped below 1. That's for a geometric (exponential) distribution of spreaders. For a uniform distribution, it should take 75% with R0=4.
It's hard to figure out what geometric distribution gives the equivalent initial R0=4 by trial and error, but maybe I'll calculate it by expectation just to get the 45% firmed up better.
When I tried a more spread-out distribution, I didn't get that much below 45% for anything plausible. I actually squared the relative weightings (so if A had 4x as many chances to spread as B, he now has 16x), and I don't think it dropped below 40%. Too lazy do walk over to double-check my notes as I write this.
My earlier comment was too optimistic - that only considered plan A (suppress then release with test-trace and enough distancing to keep R sustainably below 1) and plan B (keep imposing the lockdowns if cases grow too high). It's now clear that plan B (if we kept yo-yoing in and out of lockdown) is not obviously worse than plan C (the strongest mitigation we can manage and waiting for partial herd immunity), since partial herd immunity means 'only' 20% infection can make a difference. So we may well end up with plan C as the best option if plan A fails. Note that none of these scenarios look like a true unmitigated or weakly mitigated epidemic of the sort being considered on LW in early March.
The comments about governments literally having no plan beyond the next week, so you can't even meaningfully say whether they're trying for A,B or C seem much more apt for the US Federal government than most other places - not that anywhere in Europe or the state level has been great, but we have seen resources and thought put into post-lockdown measures.
For what it's worth, several of the more reliable models still seem to think plan A could work in EU and the UK - covid19pro shows steady exponential decline through to August.
The Good Judgment project seems to think there’s about a 50/50 shot that deaths will be above several hundred thousand
I think that, when most people use the term "herd immunity", they mean "herd immunity sufficient to get R<1 while everyone parties like it's 2019". That could require 75% to be infected, don't you think?
Right. Also:
" Shame on anyone who treats herd immunity as a boolean, rather than something that doesn’t do anything until you hit a threshold. "
This argument cuts both ways. "Herd immunity" is also not some magically threshold, after which *no one* gets infected. There's a term for it: overshoot.
From this piece by Carl Bergstrom and Natalie Dean, professors of biology and biostatistics: "Once enough immunity has been built in the population, each person will infect fewer than one other person, so a new epidemic cannot start afresh. But an epidemic that is already underway will continue to spread. If 100,000 people are infectious at the peak and they each infect 0.9 people, that’s still 90,000 new infections, and more after that. A runaway train doesn’t stop the instant the track begins to slope uphill, and a rapidly spreading virus doesn’t stop right when herd immunity is attained.
If the pandemic went uncontrolled in the United States, it could continue for months after herd immunity was reached, infecting many more millions in the process.
By the time the epidemic ended, a very large proportion of the population would have been infected — far above our expected herd immunity threshold of around two-thirds. These additional infections are what epidemiologists refer to as “overshoot.”"
Tried a few variations of the simulation, and found that if you seed a population with high superspreaders, you can indeed get to herd immunity in the 20-30% infection range.
Wrote it up for my blog at the link below. Let me know if I've screwed anything up.
http://blog.philbirnbaum.com/2020/05/herd-immunity-comes-faster-when-some.html
Regarding where the new cases are coming from:
The City of Ottawa, where I live, published a daily digest of "detailed" data up to April 29. They broke down all cases to date by where the exposure came from.
As of April 21, there were 179 cases of exposure with "no travel and no exposure to a known case." As of April 28, there were 183.
So, in that seven-day period, there were FOUR new cases with no travel/contact, out of 354 new cases total.
In other words, a maximum 4 people were infected from surfaces, grocery stores, bike paths, making deliveries, etc. As far as I can tell, that might even include working in a grocery store. That's less than 2 percent of new cases, or four cases out of a population close to one million.
That seems like great news, but nobody has commented on it.
Source: Table 4 of the digest. April 22 pdf is here: https://www.ottawapublichealth.ca/en/reports-research-and-statistics/resources/Documents/covid-19/22-Apr/Web-PDF-COVID-2019-epi-update_20200422wOutbreakEB-MA9MA.pdf
April 29 pdf is here: https://www.ottawapublichealth.ca/en/reports-research-and-statistics/resources/Documents/covid-19/29-Apr/Web-PDF-COVID-2019-epi-update_20200429-46y8.pdf
Last week: Covid-19 4/30: Stuck in Limbo
Recently: Covid-19: New York’s Antibody Tests 2, On “COVID-19 Superspreader Events in 28 Countries: Critical Patterns and Lessons”
Background Assumptions: On R0, Taking Initial Viral Load Seriously, On New York’s Antibody Tests, My Covid-19 Thinking: 4/23 pre-Cuomo Data
Spreadsheet where I do work: Access it here as read only
Deaths By Week in the 5 Big Regions:
Positive Tests By Week By Region:
Tests each week (New York’s 5/6 negative rate assumed to be same as 5/5):
Total Positive Tests:
New York: Rapidly Making It Here
The news keeps getting better, with each day seeming to be a more rapid decline in positive test rates and the implied R0. Last week I had R0 ~ 0.78, and now I have more like R0 ~ 0.74.
I believe that this reflects a real drop in the effective R0 over time. Some of that is shifts in behavior. Some of that is additional herd immunity, especially in the places it is most valuable. Some of that is selection, as the infection shifts to where it can better be contained. Some of that is that we have more resources fighting fewer infections.
That means more rapid improvement in the near term, and also more flexibility to work with before things start getting worse again. We see the opposite of what one might fear, where people start going stir crazy or get desperate for funds, and stop respecting the rules in bad ways.
We’ve still got a ways to go here. I estimate just over 20,000 new infections are still happening every day in the state. But on 5/17, unless there is a major change, I think that is likely to be down to around 10,000. I do not think Cuomo’s “Phase 1” reopening will impact R0 much.
How did New York succeed where others failed?
Was it herd immunity? That’s my main hypothesis, and what I mostly believe.
Was it that things were so bad that people actually changed behavior more than elsewhere? Cell phone data doesn’t seem to back this up enough.
Was it Cuomo’s great leadership? I guess it didn’t hurt once we got started.
Was it that New Yorkers now have enough experience that they’re making the right changes more than elsewhere? I don’t see much evidence of anything like that.
If anything, New York is by default uniquely vulnerable, as we saw early on, so that’s a huge factor working the other way. Herd immunity is the only thing that makes sense to me. I continue to believe in about 21% ever-been-infected rate for the state, which at current pace will stabilize at 23% if there is no second wave here.
That is about where I would expect herd immunity in practice to be big enough, so that makes sense to me. You have an 80/20 rule slash power law for interactions. It shouldn’t take much beyond that to get us home.
Seriously, Stop Thinking It Takes 75% Infected To Get Herd Immunity
Shame on anyone who treats herd immunity as a boolean, rather than something that doesn’t do anything until you hit a threshold. Also shame on anyone who doesn’t realize that you get partial immunity much bigger than the percent of people infected. And of course, shame once again on everyone who tries to look responsible by saying we don’t know if antibodies grant immunity at all (as opposed to be being uncertain about how long it lasts and worrying it might wear off in a year) – once again, W.H.O. delenda est.
General reminder that people’s behavior and exposure to the virus, and probably also their vulnerability to it, follow power laws. When half the population is infected and half isn’t, the halves aren’t chosen at random. They’re based on people’s behaviors.
Thus, expect much bigger herd immunity effects than the default percentages. Ignore any SIR or SIRD models that both are trying to model things under large (20%+) infection rates, and also treat all people the same. It’s garbage assumptions that yield garbage results, even if the rest of the assumptions are perfect.
Also shame to anyone who ‘warns us’ that because R0 changes that things are even harder to deal with and we won’t get proper herd immunity essentially ever. For example, the usually excellent and intellectually honest (even when I strongly disagree) Interfluidity claimed that you need to be more responsible than three quarters of those you interact with because until most of them are infected, you won’t get the herd immunity benefits.
But of course this is utter nonsense multiple ways. If your local group never gets infected because the virus doesn’t spread any more, you’re safe. Also, if your local group has safe practices you can keep R0<1 locally without any help from herd immunity.
Herd immunity will be even more helpful if people get antibody tests, and we place those who are immune in key positions.
Other Regions: Making Not Much
The Midwest and South are clearly in limbo.
The West sees a ~10% improvement in deaths, which is good. It continues to be at a low baseline rate, which is also good. And its positive test count likely reflects increased testing and a slight improvement. But this is effectively still being stuck in limbo.
The Northeast outside of New York did see a decline in positive test counts, which seems to be real rather than a decline in testing, but it didn’t see a decline in deaths. Data is indeed terrible, but we also see an accelerating decline in New York where I’ve looked in greater detail. So there’s some chance that the region has turned an important corner. That’s the good news.
That still leaves three of our four major regions in a limbo situation.
The positive testing rates went up. Some of this does seem like an indication of progress. But outside of New York a lot of the effect seems to be an artifact of where we’re doing the testing. The regions that are doing relatively well seem to be ramping up testing more than regions which are doing poorly. This does not seem like a coincidence. Areas that have their act together in some ways also get it together in others, and are more likely to do the correct amount of testing when given time to acquire it.
This Is How The Country Reopens
Not with a bang, but with a wimper.
There are some reports of lines around the block for newly opened nail salons. That makes sense, as for some people such things are considered essential services, and they went without for a long time. There’s bound to be a temporary surge in demand. However, places one frequents like restaurants and bad axe throwing ranges (and yes that’s the name and it’s a thing) are seeing few if any customers coming by. Just because you allow something to open today doesn’t mean people are eager to do or in the habit of doing what was banned yesterday.
Last week we were in a worst case scenario situation of sorts in many parts of the country. We were locked down, devastating the economy, yet we were neither gathering substantial herd immunity nor were we successfully squashing the virus. A week later, we were looking at being in the same situation except poorer and with fewer options. It is one thing to do a lock down initially, when one hopes it will allow squashing of the pandemic, and time was needed to get testing online and health care ready. Now that all further big progress on such fronts seems so far away, it seems like folly – as we do in end of life care, it looked like we are going to bankrupt the patient’s family so they can die a few weeks later.
So, because of all that and because I am optimistic about people’s private adaptations – see this post along similar lines, Dumb Reopening Just Might Work – I wasn’t feeling great about things overall, but it seemed like partially reopening was likely to be the lesser of two evils.
A week later, it is still too early to know what effect those reopenings had on infection rates. Probably very little will happen that wasn’t already going to happen. Since very little was already going to happen, that means little will happen.
Projections
There has been talk of alarmingly rising projections of infection counts and death rates. The ‘internal model’ that The New York Times asserts Trump was using, that would show hundreds of thousands of infections per day in a month, may or may not have actually been an administration model. That wouldn’t actually be a big jump, if it’s real infections rather than positive tests, since we know the death rates are undercounts and we can then extrapolate, we’re almost at that level now.
People continue to talk as if we have one-time effects rather than continuous effects. Reopening to drive R0>1 will result in ‘X deaths’ where X is not that much bigger. But if you really think a policy leads to R0>1 then you need to bite the bullet and believe it causes herd immunity levels of infection wherever implemented. How could it not? Rates of change remain a thing whether we admit it or not.
Similarly, whether or not things have just gotten better or worse seems to be driving people’s feelings about the danger level and what actions are appropriate. This is like when a ‘good economy’ is one where there’s growth and things are currently improving, and a ‘bad economy’ is one that isn’t growing and is getting worse right now, no matter what the levels of activity and wealth are. It’s emotionally resonant, but nonsense.
The Good Judgment project seems to think there’s about a 50/50 shot that deaths will be above several hundred thousand, but their definitions and categories are murky so it’s hard to pin down. In my predictions evaluations, I was willing to consider more than 300k deaths a solid favorite, and 100k deaths almost a can’t happen. I still think those are both true.
The project does have some good news – they are confident baseball will be back within two months. I could really, really use that, and I am not alone.
It still does not seem like we have the will necessary to squash this virus without help from herd immunity. Our lock down methods, absent massive infection rates or herd immunity help, get us R0 only slightly below 1. That’s not good enough, because we can’t sustain such tactics. So we are unlikely to see death rates much lower than we see now until we see a spike first.
How we do will depend on whether we are able to find sustainable ways to bring down rates of infection, and our willingness to let things run their course if we cannot do so.
The good news is there is lots of low hanging fruit we can use to improve. The bad news is that we seem incapable of grabbing it through government/collective action.
At every turn, the government’s role in this has been to try and get through the next week without things looking too bad. Actions are taken as part of a general trend of motion towards that which does not look blameworthy in the near term. No one, on any side or at any level, is building physical models, or has a plan for how to make this actually work that makes any sense. All the real plans that might actually work are in the hands of private actors.
Thus, we got lock downs because not doing so would have quickly seemed blameworthy. But there was no action taken with the time that bought us, because our system does not generate actions designed to achieve physical objectives. We’ve lost such abilities, and show no sign of being able to get them back. Eventually, private actors will figure things out sufficiently that there will be rising pressure to do useful things or at least get out of the way. We saw this for example on masks, which flipped from ‘governments conspire together to outright lie to us that they don’t work’ to ‘they’re mandatory and you’re horrible to not use one’ in the span of a week. Same will be true of antibody tests when their time comes.
I do think that ‘get out of the way’ is the best we can reasonably hope for from such people on the ‘contain the virus’ front. And it would do a lot of good. Simply getting out of the way at the beginning would have been far better than the active interference, shutting down, lying, banditry and piracy we’ve actually seen. That’s distinct from any looting and corruption on the financial rescue side. But it’s no surprise that we spent almost all the money on bribing people, and almost none of the money on health care or on research or on testing or on anything that might actually solve our problems.
If we do get ‘get out of the way’ to (vaguely and gradually) happen, then the future looks (relatively) bright. The big mystery remains, this virus is not actually that easy to catch, R0 starts only around four, we’re seeing dramatic behavior changes, why isn’t this enough?
It’s not enough, presumably, because the changes aren’t that big in some of the places that actually matter, we’re not enforcing the rules much, and we’re not doing the research to find out what actually matters, at all.
Low-Hanging Fruit
What are the easy slam-dunk things we should be doing, but aren’t doing, or aren’t doing enough?
There’s a long list. Do not consider this complete. It’s the things that I could come up with and remember today, nothing more, that I consider slam-dunk obviously correct to do. I don’t know of good arguments against any of this. I left off anything with political implications that are bad for a major party, even if they’re otherwise obviously right, and gave myself about 10 minutes. I’m also not listing anything I think we should do for economic reasons. Different post.
The basic conclusion: Yes. There’s treasure everywhere.
If I had to pick one thing to focus on one thing a private person can do, it’s we need to figure out how this spreads. One rich person, who cares, can fund the necessary work to figure this out. If you have the resources but need help figuring out how to do it, I will help you with that.
If I had to pick one thing to focus on for public choice, it would be allowing challenge trials for vaccination and also to gather other information. But if I wasn’t counting that because “ethicists” want us all to die, and I need something they would allow, I would point be our continuing failure to provide reasonable help with isolation of the sick outside of hospitals. But that’s mostly a question of where I think I could get traction.
Paths Forward
My plan is to do a weekly update with the national statistics and some of my general thoughts, and continue to supplement with other posts on other stuff, whether Covid-19, gaming, rationality or otherwise. I’m hoping these have been helpful – I’ve been extremely frustrated that it seems plausible that someone like me could be useful in this situation, since literally everyone has one job and this is it. And yet.
I also want to say I appreciate the thank yous I’ve been getting. They help me keep going. It would also be helpful, if you think these are useful, to provide signal boosts, so others can be helped as well.