There have been misunderstandings and noise surrounding the UK Government's COVID19 strategy. There are some very smart people advising the Government. I respect them greatly. Still, even after the clarifications have seen, I remain fairly concerned, for two reasons (THREAD)

There was a tendentious fight about "herd immunity", but since then the Govt's position has been clarified to be as follows. Given:

a) restrictive control measures carry social and economic cost

b) behavioral research suggesting people will only comply for a short time...

The most restrictive and effective control measures should not be imposed immediately. They should be used during a period of rapid epidemic expansion, thus maximizing the number of cases averted. This is more efficient than playing your ace on the first hand.

I see two problems with this approach:

1) There is asymmetry in costs and capacity to course-correct

2) Aggressive measures cannot be implemented immediately, and pay their greatest dividends early

1) Asymmetry
It is far easier to back off from too strong an initial response than to salvage matters after an insufficient one.

As measures are imposed, the UK can monitor case count growth. If numbers of new cases start to decline, controls can be relaxed.

But if the UK's initial response undershoots what is needed, it may become too late for even an ultra-aggressive China style response to stop the British healthcare system from being overwhelmed.

Why? Exponential growth magnifies modeling errors. If the Govt's model estimates for (a) current cases (b) control measure effectiveness or (c) time to implementation are off, the epidemic could reach overwhelming size before the Govt has a chance to course correct.

In short, overreactions are costly, but underreactions are costly too. And everything we know suggests underreactions are just as plausible as overreactions in situations like these, less reversible, and *far, far more costly*

2) Aggressive measures pay greatest dividends early

To understand why this is so, we need a tidbit from epidemiological theory.

A key parameter for any epidemic is the effective reproduction number R_e: the number of new infectious that each infectious person causes, on average, while still infectious (i.e. before recovering, dying, or otherwise ceasing to be infectious)

R_e is the product of two other numbers: the basic reproduction number R_0 ("R-nought") and the fraction of susceptible individuals in the population S/N:

R_e = R_0 * S/N

R_0 can be seen as the number of individuals each infectious person will *inoculate* prior to recovering. But only *susceptible* individuals will actually get sick. Immune individuals will not. So only a percentage S/N of the total inoculated individuals get sick, and we get R_e

Why is R_e important? Because if R_e > 1, each infectious individual more than replaces themself before recovering, and the total number of infections in the population grows. If R_e < 1, each infectious individual less than replaces themself, and the number of infections shrinks

One tough think about controlling a newly-emerged zoonotic virus like SARS-CoV-2 (which causes COVID) is that often nobody or almost nobody in the human population has substantial prior immunity. That is, at the start of the epidemic S/N was basically 1, and R_e was basically R_0

But if people who recover from a disease acquire immunity, S/N is going to fall as the disease progresses through the population. Ultimately, R_e may fall below one. If that remains so, the disease will go extinct and fail to propagate if it is reintroduced. That's herd immunity

Sweeping a few details under the rug, all the #flatteningthecurve talk you've been hearing about involves taking measures (like "social distancing") that reduce R_0, the average number of inoculations that occur per infection.

This has the effect of slowing down the rate of growth of the epidemic (all else equal) reducing the total number of cases at any one point in term and thus reducing the risk of healthcare system failure. But there's a problem: when you relax control measures, R_0 will rise again

If S/N has not fallen in the interim, a big second peak of the epidemic could result. Flattening the curve is like a controlled burn in a forest: you permit enough epidemic propagation to reduce S/N, but no so much as to overwhelm the healthcare system.

You do this by driving R_e very close to, but not below, 1, so the epidemic propagates, but very slowly, without an explosive peak, while S/N continues to fall.

Perhaps you've already noticed the beauty of this controlled burn strategy: because S/N continues to fall, as time goes on you need to reduce R_0 less and less (relative what it would be in the absence of any control measures) to achieve your target R_e.

So there's in fact no reason to hold your Ace in the hole. Your most powerful control measures should come out early, and then you can gradually relax them as the controlled burn goes on. This is more or less what the democracies of East Asia have achieved.

This avoids the asymmetry problems of trying to time things for maximum efficiency, but it also provides a clear solution to problems of compliance and frustration with control measures: people get the worst over with immediately, and things just get more relaxed from there

In short, I see both frightening risk and false economy in the UK's strategy as I understand it, and I would urge them to consider why Taiwan and South Korea see things differently.

That said, I know that thoughtful colleagues of mine, including people with many more years of experience in the field, see things differently. I write this to express concern, but I am very open to being persuaded that my concern is misplaced.

@fernpizza and I have now formalized some of the arguments I made here into a mathematical model. Please read if interested. We've attempted to make it relatively accessible, though formal https://twitter.com/dylanhmorris/status/1240050106134642695

Update to the update: a revised version of this model is now the basis of a preprint with @fernpizza, @jplotkin, and Simon Levin https://osf.io/9gr7q/ 

Twitter thread explanation here https://twitter.com/dylanhmorris/status/1246261753341673473