How long should a lockdown-relaxation cycle last? | Gowers's Weblog

]]>You definitely know how to bring a problem to light

and make it important. A lot more people should check this out and

understand this side of the story. I can’t believe you aren’t more popular because you certainly possess the gift. ]]>

So far, I have know very well that beside you and Pro. Terence Tao is not only colleague but also close friends. By the way, after looking at your both’s face carefully , I wonder that why you both look alike. It looks like two of you are brothers in the family.

Shaw prize in 2020, may is coming : you can vote one to Pro.Tao. I think he deserves to win it after many his efforts in maths.

Thank you, Pro.Gower ]]>

But if this is the case, and assuming r=3 in the absence of suppression, then a set of extreme measures which make r=0 applied for 2 days on and 1 day off would achieve the goal r=1 for ‘the dance’.

]]>covid over the coming months and years, and that is the complicated possiblities of what different parameter values lead to, a situation due just to the mathematical structure of the logistic map and not what the map is supposedly modeling. Most pronounced is perhaps the perod doubling route to chaos enacted, e.g., by changing values of the birth-death parameter studied by Sir Robert May and from which the two Feigenbaum constants were derived. Wikipedia sums up this rich behavior nicely: “bistability in some parameter range, as well as a monotonic decay to zero, smooth exponential growth, punctuated unlimited growth (i.e., multiple S-shapes), punctuated growth or alternation to a stationary level, oscillatory approach to a stationary level, sustainable oscillations, finite-time singularities as well as finite-time death.” Again these phenomenon have to do purely with the mathematical workings of the logistic map and not its applications in any practical condition such as adaptive triggering, etc. Hence, great care needs to be given to not confusing what is observed in specific applications with that of solely mathematical phenomenon. ]]>

Admittedly this was at an unacceptable number of fatalities (approximately 900,000). ]]>

The result appears if you fix the lower-threshold and optimize the upper-threshold. However if instead you fixed the upper-threshold and optimized the lower-threshold, then the optimal cycle-length will be long.

If you allow *both* thresholds to be chosen (both T and S) then, as you note, they’ll both be zero. However this isn’t practical because it ignores the cost of getting to zero given that we start with a finite set of cases.

I think instead a better approximation of the problem we face is choosing an optimal time-path of policy given some start-point and end-point. If we solve that problem then that case the optimal path will be a path of gradually decreasing strictness, without any zig-zags.

More details here:

http://tecunningham.github.io/2020/04/05/front-loading-restrictions/

]]>The first is that, in reality, infection rates are stochastic. In most of England, there are enough people that the noise term isn’t very significant. Here, we have to worry that, if S and T are small (or even not that small), the noise term will actually be driving the infection rates during relaxation phases, and, what is more, we won’t know what the noise is until it’s too late and we are in for a very long lockdown. The concern here isn’t that we start having too much infection in the population at large; rather it’s that one infectious person at a well-attended wedding could completely overwhelm the hospital.

The second is that, with limited resources and a small population, our measures of infection rates can turn out to be quite discrete. Especially if we go by something crude like ICU usage, the only possible percentages in our county are 0%, 33%, 67%, and 100%. This gets better (though not by that much) if we average across the region as a whole, but there are significant costs, socially, economically, and from a public health perspective, to helicoptering patients to the city 100 miles away.

]]>Hi Darij, that’s an interesting perspective.

Indeed testing and tracing are key points. Regarding testing, I think that the success of South Korea largely relied on very many tests and here the progress can be rapid. As for tracing, there could be also various voluntary tracing systems. See proposal 6 in David Ellis post. https://davidellis2.wordpress.com/2020/03/23/nine-proposals-for-combatting-the-coronavirus-pandemic-in-the-uk/

It is also quite possible that putting masks on can be effective.

So I am not sure that suppressing the pandemic represents a science fiction.

The tradeoff is also an interesting issue. Chaos, massive unemployment and devastating economical consequences, are expected both ways. And I am not sure why closing the borders for one year (if it is necessary at all) is a big deal.

If the number of casualties among risk groups is as reported then not taking the harsh steps needed to suppress the pandemic is also morally wrong.

]]>@Gil Kalai: “should not be contemplated” is rather wishful thinking, given that suppressing the virus would require either vaccination (>1 year away, probably much more before it can scale up to whole countries) or a well-functioning contact tracing system (won’t happen any time soon in Europe due to the abysmal slowness and incompetency of government IT; probably won’t happen in the US as long as FDA and CDC are running the show). Not everything that works in Singapore or Israel will work in the West; progress is not a linear order. Of course there is always the possibility of science doing miracles, but before they happen, successful suppression is just science fiction. And if waiting for this science fiction to happen results in a year of mass joblessness, closed inter-European borders and all-around chaos, it’s far from clear it’s a good tradeoff.

]]>Tim said: “The alternative would require massive overload of the NHS, so I don’t think it should be contemplated.” Let me add that waiting for a large percent of the population to be infected should not be contemplated also because of the large number of casualties even without taking into account the NHS capacity. As both China and South Korea realized the only viable option is to suppress the disease well before herd immunity of any kind.

]]>Thanks for letting me know about this.

]]>This short paper provides a rationale for 4 day work and then 10 days lock-down

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