For some reason I’ve been reading a lot of Italian epidemiology reports lately, and my Italian isn’t very good. So I found myself at first assuming that counts of “ricoverati” cases were those who had recovered. And that made it really confusing that this document estimates the median time from “ricovero in ospedale” to death (4 days). I had to look it up to discover that ricovero actually means hospitalised (and more generally, sheltered).
An epidemiologist says, “A new pandemic will definitely sweep the world some time this century. But you won’t know until the day it starts when it will be. So you’d better start preparing now.”
The president is downcast. He doesn’t like preparing, but he also doesn’t like when the stock-market falls and people on TV blame him for millions of deaths and blah blah blah. What can he do?
His son-in-law comes to him and says, “I read a book on this. This prediction of an unexpected epidemic can’t happen. Imagine it’s 2099 and there hasn’t been a pandemic yet. Then people would know it has to happen in 2099. So it has to happen earlier. But now, suppose we get to 2098 without a pandemic. We know it can’t happen in 2099, so we would know for sure it must be 2098, which would contradict what the so-called expert told us.” And so, step by step, he shows that the unexpected pandemic can never happen.
You know the rest: The president disbands the National Security Council pandemic preparedness team and writes a celebratory tweet. And then in 2020 a pandemic arrives, and the president announces that “this is something that you can never really think is going to happen.”
My recent post suggesting that the government may have some reasonable thinking behind their go-slow-but-not-too-slow strategy had two underlying errors:
- I assumed they knew what the NHS capacity is, and were trying not to linger too long in the period where there is plenty of spare capacity. In fact, resources already appear to be overstretched, particularly protective equipment (PPE), even though the epidemic has barely started, and there are just a few thousand cases in total so far.
- I neglected to reckon with — what was otherwise obvious to me — Johnson’s Churchill complex. Johnson doesn’t have all that much in common with Churchill, but one thing the two do share is a mania for all manner of harebrained wheezes rather than careful dependable planning. Keynes famously said “Worldly wisdom teaches that it is better to fail with the crowd than to succeed unconventionally”. Johnson is one of those rare individuals who would rather fail unconventionally — or, at least, is willing to hazard a strong risk of failure for the compensation of being seen as brilliantly unconventional.
Now the government says they miscalculated, after a paper from Imperial College’s Covid-19 Response Team found that the previous strategy would exceed available ICU capacity by a factor of 8! Did they misplace a decimal point? So suddenly the schools, gyms, and everything else that was announcing plans to cope with staying open through the epidemic is shutting down.
I find it genuinely shocking that the UK does not have a strategic reserve of PPE and ventilators, particularly the latter, as the shortage of ventilators was widely discussed in the press in 2009, in the context of the H1N1 pandemic.
Anyway, I’m glad I’m not in the US…
It would be a drastic understatement to say that people are confused by the official advice coming with respect to social-distancing measures to prevent the spread of SARS-CoV-2. Some are angry. Some are appalled. And that includes some very smart people who understand the relevant science better than I do, and probably at least as well as the experts who are advising the government. Why are they not closing schools and restaurants, or banning sporting events — until the Football Association decided to ban themselves — while at the same time signalling that they will be taking such measures in the future? I’m inclined to start from the presumption that there’s a coherent and sensible — though possibly ultimately misguided (or well guided but to-be-proved-retrospectively wrong) — strategy, and I find it hard to piece together what they’re talking about with “herd immunity” and “nudge theory”.
Why, in particular, are they talking about holding the extreme social-distancing measures in reserve until later? Intuitively you would think that slowing the progress of the epidemic can be done at any stage, and the sooner you start the more effective it will be.
Here’s my best guess about what’s behind it, which has the advantage of also providing an explanation why the government’s communication has been so ineffective: Unlike most other countries, which are taking the general approach that the goal is to slow the spread of the virus as much as possible (though they may disagree about what is possible), the UK government wants to slow the virus, but not too much.
The simplest model for the evolution of the number of infected individuals (x) is a differential equation
Here A is the fraction immune at which R0 (the number that each infected person infects) reaches 1, so growth enters a slower phase. The solution is
Basically, if you control the level of social interaction, you change k, slowing the growth of the cumulative rate parameter K(t). There’s a path that you can run through, at varying rates, until you reach the target level A. So, assuming the government can steer k as they like, they can stretch out the process as they like, but they can’t change the ultimate destination. The corresponding rate of new infections — the key thing that they need to hold down, to prevent collapse of the NHS — is kx(A–x). (It’s more complicated because of the time delay between infection, symptoms, and recovery, raising the question of whether such a strategy based on determining the timing of epidemic spread is feasible in practice. A more careful analysis would use the three-variable SIR model.)
Suppose now you think that you can reduce k by a certain amount for a certain amount of time. You want to concentrate your effort in the time period where x is around A/2. But you don’t want to push k too far down, because that slows the whole process down, and uses up the influence. The basic idea is, there’s nothing we can do to change the endpoint (x=A); all you can do is steer the rate so that
- The maximum rate of new infections (or rather, of total cases in need of hospitalisation) is as low as possible;
- The peak is not happening next winter, when the NHS is in its annual flu-season near-collapse;
- The fraction A of the population that is ultimately infected — generally taken to be about 60% in most renditions — includes as few as possible of the most at-risk members of the public. That also requires that k not be too small, because keeping the old and the infirm segregated from the young and the healthy can only be done for a limited time. (This isn’t Florida!)
Hence the messaging problem: It’s hard to say, we want to reduce the rate of spread of the infection, but not too much, without it sounding like “We want some people to die.”
There’s no politic way to say, we’re intentionally letting some people get sick, because only their immunity will stop the infection. Imagine the strategy were: Rather than close the schools, we will send the children off to a fun camp where they will be encouraged to practice bad hygiene for a few weeks until they’ve all had CoViD-19. A crude version of school-based vaccination. If it were presented that way, parents would pull their children out in horror.
It’s hard enough getting across the message that people need to take efforts to remain healthy to protect others. You can appeal to their sense of solidarity. Telling people they need to get sick so that other people can remain healthy is another order of bewildering, and people are going to rebel against being instrumentalised.
Of course, if this virus doesn’t produce long-term immunity — and there’s no reason necessarily to expect that it will — then this strategy will fail. As will every other strategy.
[Cross-posted with Statistics and Biodemography Research Group blog.]
The age-specific estimates of fatality rates for Covid-19 produced by Riou et al. in Bern have gotten a lot of attention:
These numbers looked somewhat familiar to me, having just lectured a course on life tables and survival analysis. Recent one-year mortality rates in the UK are in the table below:
Depending on how you look at it, the Covid-19 mortality is shifted by a decade, or about double the usual one-year mortality probability for an average UK resident (corresponding to the fact that mortality rates double about every 9 years). If you accept the estimates that around half of the population in most of the world will eventually be infected, and if these mortality rates remain unchanged, this means that effectively everyone will get a double dose of mortality risk this year. Somewhat lower (as may be seen in the plots below) for the younger folk, whereas the over-50s get more like a triple dose.
This article about the effect of the coronavirus pandemic on air travel mentions social-media criticism of millennials (of course!) for ignoring public health advice by taking advantage of lowered airfares for inessential travel. It occurred to me, though, that the well-publicised observation that the virus seems hardly to affect children and young people at all may create different incentives for different age groups.
And that reminded me of The Subtle Knife, book 2 of Phillip Pullman’s fantasy trilogy His Dark Materials about Oxford scholars (and children) exploring the multiverse. A significant portion of that book is set in a parallel world that has been overtaken by “spectres” that attack and devour the minds of adults, but leave children unharmed. So children run wild and the few remaining adults are in hiding.
No further comment…
In trying to compose an argument for why Democrats’ best hope for defeating the incompetent septuagenarian autocratic billionaire Republican in the White House is to nominate a highly competent septuagenarian autocratic billionaire (former) Republican of their own, Emily Stewart at Vox — jumping in to extend Vox’s series on the leading candidates in the Democratic presidential primary with the case for late entrant Mike Bloomberg — has some reasonable points, mixed in with one very odd accolade:
Under Bloomberg, New Yorkers’ life expectancy increased by about three years.
Not that this is false, but we must recall that Bloomberg was mayor of New York for 12 years. As pointed out by Oeppen and Vaupel in a Science article that appeared in 2002 (the first year of Bloomberg’s mayoralty), life expectancy at birth in the most economically advanced countries of the world has been increasing at an astonishingly steady 2.5 years per decade since around 1840. If we had then predicted how much increase we should expect over 12 years, we should have said… three years. Indeed, looking at a few comparably wealthy countries chosen more or less at random over the same period we see life expectancy at birth as follows:
Mike got it done!
To be fair there are two exceptions to this trend: Japan, which had the highest life expectancy in the world in 2002 still had the highest in 2014, but it had gained only two years.
The USA, which had the lowest life expectancy at the start (among large wealthy countries), at 77.03, fell further behind, to 79.06, and has since actually decreased. So I guess you might say that Bloomberg has shown his ability to thwart the destructive trends in the US, and make it, as he made New York, as successful as an average West European country. Which doesn’t sound like the worst campaign platform.
One of the newspaper covers promoting pro-Brexit celebration:
It’s hard to miss that the jubilant lady draped in the Union Jack has a US flag right behind her. A message to those who still suppose Brexit will bring “independence”. (In case they didn’t get the message when the Prime Minister stood up in parliament and pretended to take Jared Kushner’s Middle East “peace plan” seriously.)
And in case any Jews or Muslims might have thought they would be part of this “glorious new Britain”, they have a fucking CRUSADER in their masthead!
A little-publicised development in statistics over the past two decades has been the admission of causality into respectable statistical discourse, spearheaded by the computer scientist Judea Pearl. Pearl’s definition (joint with Joseph Harpern) of causation (“X having setting x caused effect E”) has been formulated approximately as follows:
- X=x and E occurs.
- But for the fact that X=x, E would not have occurred.
Of course, Pearl is not the first person to think carefully about causality. He would certainly recognise the similarity to Koch’s postulates on demonstrating disease causation by a candidate microbe:
- No disease without presence of the organism;
- The organism must be isolated from a host containing the disease ;
- The disease must arise when the organism is introduced into a healthy animal;
- The organism isolated from that animal must be identified as the same original organism.
I was reminded of this recently in reading the Buddhist Assutava Sutta, the discourse on “dependent co-arising”, where this formula (that also appears in very similar wording in a wide range of other Buddhist texts) is stated:
When this is, that is;
This arising, that arises;
When this is not, that is not;
This ceasing, that ceases.
I shudder to think…