The Corona Virus

[NichG]

Hey Nich, I feel like we may be talking past each other a but, and I'm not sure what the underlying point we actually disagree on is. I'm happy to address your above post point by point if your prefer, but I wonder if we might be better to reset.

My main point is that it is not obvious that isolation was (or is) the best reaction to Covid 19 because isolating for a couple of months or so will cause significantly more economic harm than taking a more light touch approach (even if that means the response is more protracted. My impression is that some people consider that the elimination of the virus is the only (or at least, by far the most important) factor to be considered when we decide what the response should be, when I think the reality is that we should weight that against other factors. My point applies whether we are talking about what a given country should have done, what a given country should do now, or what a given country should do next time.

I take your main point to be that in an ideal world countries should co-operate by taking a similar approach to one another at the same time - to avoid some countries from eliminating the virus only to have it reintroduced. Am I right that this is your point? If so, I agree that you are right in theory, but I don't think what you are suggesting is a practical reality.

Where we may disagree (and I'm not sure) is if where you say countries should co-operate you mean for them to co-operate in a certain way? I take it you are not saying that countries should co-operate to take a light touch and let the virus run its course? Is that right?

There's two points here, which I want to keep disentangled. The first point is, what is the value of lives versus GDP lost? I don't want to get into that point here because it's not really a point of fact, it's a values question and it strays into politics.

Instead, I'm saying that given however you'd like to relatively value lives to GDP, there's still a hierarchy of strategies where some strategies are inherently wasteful and others are not. If you tell me 'I'm willing for us to sacrifice 5% GDP for an intervention strategy, do the best you can' or 'I'm willing to sacrifice 50% GDP for an intervention strategy' or whatever, some plans will get you more benefit for the cost than others. That second point is what I'm focusing on here, because it isn't a question of values or politics, just a question of dynamics.

Now, there are things about the structure of the problem that I'm concluding from how growth processes work, and these may be points of disagreement, though if you want to disagree with these I'd prefer you say why rather than just 'it's an assumption!' or something like that. These are based on mechanistically what a virus is and how viruses spread.

1. There is a sharp boundary in the pay-off structure where on one side of the boundary you have the cases where Covid is driven extinct, and on the other side you have the cases where it is not. The mechanistic motivation behind this is that if you don't drive it extinct then it can still spread in susceptible people until the point of herd immunity + overshoot; or if immunity is temporary, it becomes endemic and incurs costs for every year for the rest of our lives. So a small change in the effectiveness of a strategy can make for a large change in the payoff. A corrollary of this is that the distribution of payoffs is going to be strongly bimodal - either you end up in the 'we drove it extinct' lobe or you end up in the 'most of the population was infected' lobe.

2. Strategies which result in extinction can be local in time, whereas strategies that target mitigation have to extend for the duration of the pandemic. This is the motivation between test/trace/isolate and contact tracing strategies in general - so long as the pandemic is taking place in small number outbreaks, extremely minor local interventions can drive it extinct. Once it's at the level of community transmission, you first have to get it down to that level where percolation fluctuations can have it locally die out completely.

So the point of this is that half-measures are likely to be wasteful. If you do a harsh intervention and you don't kill Covid, you should have done a light intervention. However, if you do kill Covid, it's worth orders of magnitude more in payoff than if you don't. There's a secondary calculus of how long it takes to kill Covid, where taking longer results in more deaths in the end, but that effect would be second order to the first order effect of kill-or-not.

So the important conclusion: Given all of that, if you're going to do harsh measures, its important that everyone do harsh measures in sync with one another, because otherwise you're going to pay the price but not get the payoff.

Now the more subtle point that does require dipping a little bit into the values discussion is, should anyone at all do harsh measures or should we just give up and say 'we accept that the entire population will get Covid?'. I say dipping because I don't want to debate if we should or not, I just want to point out that:

1. If you and someone else have wildly different valuations in how you assess the value of GDP versus lives, the nice thing about GDP is that it's fungible. So someone who values lives more can pay you to value GDP less, and so on. This is tongue-in-cheek at an individual level, but this point is important if we're talking about cooperation between countries. Because a country who is reluctant to shut down because of economic disadvantage could be subsidized by a consortium of others to change their policy, in order to make the economic impacts fair. So pointing out the most extreme case of economic deprivation isn't a counter-argument to a cooperate-harsh strategy.

2. If we use the behavior so far to estimate different countries' values as to GDP vs lives, we can use that to bound the distribution of payoffs needed to accomplish point #2. Countries have been willing to lock down for 6 weeks or more so far, so at least in the present valuation of things, we can get some idea of costs that countries are willing to pay. Individual values may deviate strongly of course, but at least in a theoretical and purely economical argument, the cost of subsidizing those individuals in order to be fair to them is relatively small at the country level.

So under those points, the cooperate-harsh strategy seems to be on the table in terms of total costs of that strategy. The counterargument to this would be that synchronizing harsh measures would increase the cost of implementing or bearing those measures, not 'harsh measures are expensive' - to say that NC-harsh is a better strategy than C-harsh, C-harsh has to cost more, not just cost the same.

There is another thing which has come up, which is 'would even C-harsh drive Covid extinct?'. We do have examples of places that have locally wiped out Covid or reduced levels to the degree that contact tracing can manage outbreaks, so I'd argue that even at the level we're at now, suppressing or wiping out Covid isn't a 'physical' impossibility - there are actions that could be taken that would do it without the total destruction of the country that implements them. So I'd say the evidence strongly rejects the idea that we have no recourse but to live with Covid and ride it out.

I'm not particularly stuck on C-harsh meaning lock-downs as envisioned by this or that country so far, but I would argue strongly against C-moderate or something like that - because the benefits fall off sharply as the effectiveness of the intervention falls off, due to the whole growth process thing. So generally pushing harsher for a shorter time period is going to be more effective than pushing gently for a long time period for the same cost paid.

There's a whole separate discussion about estimating risks and the values thing and so on as well, but I think all of that is mostly separate from these points. If we want to dig into that, it isn't too hard to model this kind of thing, so I can spin up a multi-locus SEIRS model or something and we can measure just what the difference in effects are between synchronized R0 reductions and desynchronized R0 reductions, or what the distribution of risks are consistent. From what I can tell, the data we have right now does not bound the parameters very tightly - I can get anything from 9000 to 1.4 million deaths in Sweden on a ten year timescale based on the existing death data. The parameter that is responsible for the biggest part of that swing is whether or not we develop long-term immunity (though there's some other stuff with the interaction between lag times to death versus overall IFR - the longer the lag time between infection and death, the more lethal the fit needs Covid to be to explain the existing data). But I think this is probably a tangent.

Edit:

Okay, I've played around with simulating this now. There's an extra factor which seems to be pretty important, which is: what is the distribution of times between infection and recovery. If that distribution is Poisson, then you need a much longer intervention period than if it's Gaussian. Mechanistically I'd expect it's Gaussian since if your immune system doesn't adapt to it quick enough, you just die of it, but if it does turn out to be Poisson then synchronized vs asynchronous interventions matter a lot less.

Edit2:

Coordinating the durations of quarantines seems to have a bigger effect than coordinating the timing. At least in a multi-locus SEIRS model, it looks like a sharp phase transition starting at a certain severity of intervention, beyond which the cooperation effect starts to matter a lot but below which there's no perceptible difference.

Hold on this, double-checking things.