I promised myself that I wouldn't upset anyone by airing my petty little thoughts on the global pandemic - after all, everyone is trying hard, doing their best, and some people are really performing absolute heroics in the public interest. And, of course, we have the top brains in the world concentrating on the problem, and surely we can be confident of the wisdom and the organising abilities of our elected leaders?
You may harbour some concerns about whether the leaders can actually hear the top brains, but I would hesitate to be unconstructive about the state of play.
Since I am starting to believe there is a very good chance that I may not survive this episode of world history, I'm beginning to lose touch with the reasons why I should keep quiet about it, but I shall avoid being rude about anyone in particular. This note is merely the musings of the sad little soul of an old mathematician, and I don't expect anyone to agree with me, nor be concerned about what I have to say - it's OK.
When something bad happens, reaction to it calls upon a lot of things. Some of these things will have needed some kind of investment of funds and effort before the event - preventative stuff. Identifying potential risks, putting in place rules and regulations to minimise the likelihood of a disaster; if we focus loosely on catastrophic building fires, as an obvious example, we might have implemented strict control of design and construction standards, of the safety of materials used, sufficiency of emergency exits and lighting, documented procedures for using all these - and I mean maintained, tested procedures. We need to ensure that people who are at risk know what they need to do, or at the very least know where to find out quickly. There should be a good level of awareness of how to cope with an emergency, plenty of guidance information, and sufficient investment in rescue services and equipment is essential, obviously. The plans should be as complete as they can be, and should, if possible, be reviewed as part of the normal routine of making changes, and - if at all possible - they should be tested periodically. There's lots of this - far more than I can think of off the top of my head - things that have to be done in advance, just in case, procedures that have to be followed, if it happens, and trained, fully equipped rescuers who will turn up promptly and do the business in the regrettable circumstance of the bad thing happening.
All pretty obvious, really. I believe that in the UK we tend to concentrate on the end of the chain - we pride ourselves on our ability to perform well in an emergency, rather than in our talent for planning in advance to avoid problems happening at all, which is traditionally seen as rather unrewarding and maybe a bit negative. If the disaster comes, we film the heroes from the rescue services in action, we have a victory parade, we award medals, we may have a day of national mourning if we really have to. It's cheaper that way.
(1) it probably won't happen - let's hope not
(2) if it does, we'll make a huge splash about the heroics of the rescuers (quite rightly so, by the way - absolutely right on) - that's better politically and for uniting public support. The Daily Express loves that stuff.
(3) if there's a public enquiry afterwards, with a bit of luck we will no longer be in office to be held accountable or have to stump up with the money, or we may be able to spin it somehow to get off the hook
OK - that's all theory, and there's nothing particularly clever about it. That should be reassuring - we don't know for sure, of course, but we would certainly expect that things will be handled as well as possible by the people in charge.
I follow the daily bulletins in the UK media about the progress of our pandemic lockdown. It's been very harrowing, but thus far the course of action has been pretty much forced by events. We have been reacting - that's the bit we think we are good at. The next bit is going to be scaling the thing back, which will require decisions to get life going again, being careful not to have a new wave of infections as a result. This will take judgement - at which point my confidence in the leaders starts to leak - and, let's face it, we haven't done this before, so there is no manifesto to act out.
Like everyone else, I have to watch all this with as much hope as I can muster. A lot of faith seems now to be pinned on the Reproduction Number - R0, as it is termed, as an indicator. Sometimes, I find, mathematics can be reassuring - if you can measure something you can understand it - maybe even control it - so I spent a little time reading about this. Crudely speaking, as you will certainly know, it is a number which compares the number of new infections in a unit time with the number of people in the population who were already infected during the same interval. If you can get the value to less than unity, then that's good. We're not exactly sure what the consequences of R0 = 1 would be, but they would sure as hell be better than R0 = 10.
OK - it's not quite like this - we are considering rates of change here, so there is some calculus in there, and since we are considering variations in exponential growth functions there are a few natural logarithms too, but the spirit of the thing is that we have to divide one number by another, and try to get as small an answer as possible. This is obviously important, so I am paying attention.
The number on the top of this fraction - the new infections - is it known, then? How accurate is it?
Well, we only started widespread testing some weeks into the pandemic. We know about people who are in hospital, and we now know more about other categories - health workers, some other key workers, we are starting on residents and staff in care homes for the elderly (at this point I know more about the current situation in Scotland rather than the entire UK, but Scotland is normally the same as the rest of the country, maybe a few weeks behind). There are a whole pile of other people of whom we have no record at all:
* people who caught the virus and, as is very common, never knew - showed no symptoms at all, though they might well still be a source of infection to others
* people who became ill, and thought they might have Covid-19, but did not become sufficiently unwell to contact their doctor or go into hospital - they just quietly recovered, and thought they might have had it
The total of these two categories is certainly considerably larger than the people who have tested positive, so we have, at best, a measure of the size of the very small tip of an unknown iceberg.
Righto - what about the divisor, the number on the bottom of the fraction? - do we know how many people were already infected during the study period? Well no - of course we don't - given the tiny coverage provided by general testing, and the lack of understanding of how this virus behaves - how long are affected individuals infectious? - what is the true nature of the immunity which comes from recovery? We don't really know.
There are other details about what statistics we have on people who leave the infected population by either recovering or dying, but that is, once again, going to be a small number compared with people we can't identify and don't count. Let's not fuss about the details - the truth is that R0 is based on a mathematical function involving the comparison of one number we do not really know and another number which we also do not know. I do not find that comforting. We will be able to see if the number of people who die in hospital drops, and we can make some estimates of what has contributed to any change in that, but R0 looks like a dead duck to me, unless we know a whole lot more than we possibly can at present.
Overall, I'd be happier if someone would admit that R0 is no real help to us at the moment, and explain what else we can use. Next time the day's government spokesman makes a big deal about R0 dropping I shall be quietly confident that he is bluffing - there may be some number that he and his colleagues refer to as R0, but I don't believe it is anything which is of any real application to the public at large.
How about the entrails of a goat?
"Sad little soul of an old mathematician?" Tony, say it ain't so! We still count(!). Perhaps not as effortlessly as in our younger days but experience ought to count for something. Right?
ReplyDeleteWatching this all unfold has been of great interest to me as well. Of course, I don't believe we really have a solid handle on either the numerator or denominator in the infection rate calculus. We may never know. Testing more of the population is critical to arrive at a better estimate but testing has problems too. A test is a snapshot in time. One can be clear one minute and infected the next. Well, infection transmission may take longer than a minute but you understand.
What I find of particular interest is that this offers a rare instance in which the effects of exponential growth are recognized by non-scientists. Even viewing cumulative infection counts on a logarithmic scale has a certain cachet.
Some governments are more adept at bluffing than others.
Hi Jon - no, I'm increasingly convinced that my view is not required. Not to worry.
DeleteAfterthought - I've always been intrigued that lack of numeracy has always been sort of acceptable, socially. If someone says (in the right accent, naturally), "Oh I've always been hopeless with figures", then everyone laughs - it's kind of faint self-deprecation, though not in a very damaging way, and there is always the implication that we employ common tradesmen such as accountants to do that sort of thing. It would take some considerable social skill to say, "Of course, I always had difficulty reading" and still raise the same relaxed laughter. Seems odd, that.
DeleteFunnily enough I was having exactly the same conversation with Mrs E yesterday (sad old tax consultant and statistician here) and I completely agree with your logic R0 is a really useful indicator, if only we knew what it's value actually was.
ReplyDeleteI'm left with the feeling that the only true indicator we can trust is the one we seem to be dancing around. The comparison of annual deaths per million in total pre and during the pandemic. If all other influencing factors are generally constant than the difference is C-19 deaths. Except the difference isn't but it can be estimated with some certainty. Road traffic deaths are down but will probably follow the same ratio of deaths per total mileage travelled, Deaths from work related causes should also be down as furlough reduces the number of people actually in workplaces. Deaths through household accidents are probably increased as are deaths due to not seeking medical support and sadly I suspect suicide rates will be up due the self-isolation. The real answer is something we wargamers understand only too well when trying to garner hard and fast facts about the reality behind our hobby is 'we don't know for sure', we just like to pretend that someone knows and I don't think they have anything better than estimates.
Remember the quote from (I think Oscar Wilde), @It has come to my attention that politicians use statistics rather like a drunk uses a lampost, more for support than illumination!'
Stay safe Tony and nil illigitimus carborundum.
Mysteriously, my reply to this has vanished without trace - so I'll try again! I think we can reasonably expect lighter mortality rates for a while after the Covid virus recedes. A lot of weaker, older and infirm people who might have been likely to die over the next few years have been taken early by the pandemic. This is a very sad subject, but my actuarial training has given me a rather analytical view of death rates. Mind you, I'll be furious when I have to go myself.
DeleteThere once was a bear
Who just didn't care,
Whether he lived or he died.
But when he was dead,
He lay in his bed
And he cried and he cried and he cried.
Along with other ways of passing time, we've been watching a British show about a group of archaeologists and other experts who get together periodically to blitz a site that needs looking at but isn't funded and try to find enough evidence to convince someone to do a proper job of it.
ReplyDeleteThe last show included an unexpected find of flint tools from before the last Ice Age so more than 2,000,000. I like to take a perverse bit of pleasure in thinking that though I'll be lucky to get more then 20 years, if that, 30 tops, 2,000,000 years after my departure, some distorted descendent of us will probably still be infesting this part of the universe, causing problems for every one else.
Good stuff - I do worry a bit about archeologists - one of the few sciences which systematically destroys what it looks at.
DeleteI really don’t get the ‘unity during the War argument’. There were many disagreements within and between parties, and between military, air and naval staffs and the government, and strikes. None of that led to surrender. The side that lost was the one that famously followed the leader’s line.
ReplyDeleteOh and policy was decided in a coalition. When faced with existential crises, NOT forming some type of coalition is the most dangerous form of playing politics.
Coalitions are useful - sometimes essential. I do agree with Robbie that the present amount of criticism of the Govt from the mainstream press (and it's still heavily politically slanted) would probably not have been tolerated during WW2. Blessed are the know-alls who don't have to make any actual decisions, for they shall fill up the gaps in Hell (with luck).
DeleteIn NZ it's thought that about 500 people arriving from overseas (nearly all of whom were Kiwis) managed to infect another 1,000. They key to killing it off was four things: a draconian lockdown of 6 weeks duration, closing the borders, and massive efforts to ramp up testing and contact tracing capability. We're now down to zero cases, but it's only staying that way, or very close to it, because everyone arriving in the country (which isn't very many) is being imprisoned in an Auckland hotel for two weeks. This has killed the travel and tourism industries stone dead, which is no trivial thing for a country that had little else to export other than dairy products, but the alternative didn't bare thinking about. We're all going spectacularly broke, but at least there'll be plenty of cheese and beef sandwiches.
ReplyDeleteHope things continue to go well, WM. In Scotland the start of easing-off on the lockdown will probably start a week or two later than in England. Not such a bad idea since the Scottish figures haven't started to improve to the same extent yet. There are some people who just assume we're being difficult (of course), but it also gives a chance to see how things go in England first. I'm a little concerned that the economic pressure to re-open businesses will be driven by Covid improvements in London, though Yorkshire and a couple of other places may not be quite ready for it yet - if it's possible, each region should decide for itself. Don't mention Florida.
DeleteDifferential regs in the two countries is a bit complicated - my youngest son is likely to go back to school in a couple of weeks - he's at school in England (about 10 miles over the border), and we could be in a position where it will still be against the regs in Scotland to travel to school! We'll see how it goes. I'm pretty sure he will come home from school and infect me, after all my weeks of hiding!
Good rant. The thing I've been intrigued by in New Zealand is the way that the narrative was controlled by two people, the PM and the Director-General of Health. A masterclass in studied manipulation of the populace. All in an excellent cause of course, but quite a thing to witness, and somewhat unsettling.
ReplyDeleteWelcome, young sir. As I remember, there was some sort of rule of thumb for emergencies which was that the preparations and the procedures should be sorted out by a committee of appropriate people, to optimise knowledge, but the leadership in an actual emergency should be by a single person, to speed up decision-making - two coxswains in a lifeboat is probably one two many.
DeleteReminds me (digression) of another tale I heard about an experiment they tried in the USAAF, whereby bomber crews were trained so that each individual was an expert in something they would need if the plane forced-landed in a hostile environment. For example, someone might be an expert in finding water in the desert, someone might be an expert in first aid, someone would know which plants could be eaten - like that. As I recall it failed because officers wouldn't take direction from someone of junior rank, not necessarily because they thought it was insubordinate, but because they felt it was their job to take responsibility if the crew's lives depended on it. This story may be bunkum, of course, but you could see how it would take on a life of its own on management training courses.
Your points about using R0 as a decision making tool are valid, and we won't begin to get into the concepts of positive and negative predictive values of tests, which are dependent both on the test performance itself, and the nature of the population tested. ALL my medical students have to endure a discussion of the principles of population screening, which are very important for a Family Physician to understand.
ReplyDeleteGiven the uncertainty in estimating the true R0, it's biggest utility is as a concept to explain to general population what it takes to slow and/or stop an epidemic, as opposed to letting it run rampant, and how that relates to the public health measures recommended.
The total impact of the pandemic on mortality is difficult to estimate given the diverse impact of the effects of the efforts to curtail it (decreased deaths from accidents, increased menatl health related issues, and many others. However, if we just look at death rates in an area reasonably heavily impacted (the UK, NY-NJ-CT in the US), the death rate is roughly twice the usual. That's a pretty big increase. Certainly at the Hospital level, the impact is very obvious and profound to us. It is always easy to criticize actions of those in charge, but for the most part the early actions in the US and the UK were far less than they should have been by reasonable standards. On the other hand, the calculus of public health effects versus economic hardships is an extremely difficult one. Done "right", that is the proper providence of political systems; both to make those hard choices, and to bear the consequences of the results.
Even more than lack of numeracy, lack of basic understanding of probability and statistics is very disabling in understanding our world. Wargamers at least have some exposure to that by the nature of our games (I derived Pascal's Triangle in High School when thinking about probabilities related to dice rolling!). As much as I thoroughly enjoyed learning trigonometry and calculus, those in non science related fields have little need or use for them; *everyone* possible should understand the basics of probability and statistics, though. In my not particularly humble opinion, of course! :-)
Peter - I have too much to say for a single comment, so I'll try to spread it over two!
DeleteThanks very much for taking the time to comment here - I realise you are very overworked, and very close to the problem, and I hope you will observe that the last thing I intended was to imply criticism of the people who are working to dig us out of all this. My admiration for what is being done in that area is boundless.
What is possible, however, appears to be restricted in its effectiveness by the rules and the shortages which are imposed on them by what has gone before.
I really do understand that R0 as a principle is invaluable and necessary - may the medical students of the future grasp it firmly - my gripe here is entirely aimed at what seems, in the UK at least, almost as a deceit - passing off a theoretical concept as a practical and useable indicator, to be monitored and publicised as some kind of weapon we can use.
It is useless and irritating to spend a lot of time lamenting all the things that should have been done in advance of the real emergency. It's hard now to find truth and clarity in all the obfuscation and arse-covering, but it does seem to me that - maybe in the wake of Ebola, or Aids? - the Swedes and the Germans and the South Koreans and a few others actually thought about the big question: what if this happened again, really seriously, and it happened here? How could we cope? What would we need? Is there anything we could have ready, in the cupboard, just in case? Whatever the reality, these nations seem to have been able to start extensive testing very quickly after Covid arrived, and they had pre-ordained procedures in place to check on the travels and the contacts of anyone who tested positive - whatever the shortfall of the tests, that must be the correct approach. They also seem to have had stores of protective clothing and materials, and a good handle on the hospital space and the trained staff which could be deployed. Perhaps they were lucky, perhaps things will deteriorate for them later on, but they tried, they were businesslike, and it looks as though what they did has given them some advantages.
The following clip will be familiar to you, but it is almost painful to watch now - it makes a nonsense of the "someone played a dirty trick on us" bluster, and also it gives a reminder of a wisdom, and a certain dignity, which seems very remote now:
https://www.youtube.com/watch?v=pBVAnaHxHbM
In Britain we had minimal arrangements for public testing - it's now been worked on (emergency mode - play to our strengths?) and something is happening, but for a while the policy and the lack of resources were terrifying.
Well, in the US, in the aftermath of the SARS-1, Ebola, and others we had a pandemic task force and a VERY detailed playbook for how to deal with a potential pandemic. The current occupant of the White house disbanded the task force shortly after he took up residence there, and ignored everything in the playbook. Yes, moron, you ARE responsible. Not to say that a perfect job is even possible with a new situation with a great many unknowns, but most of his actions made things worse, and continue to do so despite his blatant falsehoods.
ReplyDeleteAs far as your mother in law, I have patients in 2 nursing homes, my mother in law is 94 and in assisted living, and my mother, 96, just entered a skilled nursing facility for short term rehab after a fall yesterday. Their situation was and is challenging, to say the least.
They were the first places in the US to go on lockdown, as their vulnerability was obvious after the debacle at such a facility in Seattle early on in the US experience. They really could NOT have tested everyone in those facilities who was asymptomatic - there simply were no where near enough tests at first. Before starting my stint in the hospital, I was ordering the tests, and we had a detailed protocal to follow. No symptoms, no test. Not high risk, no test, we monitor you closely (by phone/telehealth). The whole issue of the likelihood of asymptomatic transmission was very debatable at that time. We couldn't even test everyone admitted into the hospital until mid April. We are in much better shape now with testing, but could have been there a month earlier had the US acted more appropriately. The next question is how often to test asymptomatic persons in that setting - once a week? Every 2 weeks? You get the picture. It wasn't even possible to just test new admissions initially. Second, who do you think got all the protective equipment? Right! The hospitals, and with them scrounging the planet for supplies it was very hard for these facilities to compete (same for ambulance crews and rescue squads). That compounded the problem of controlling exposure of staff and patients. The staffing levels in nursing homes is far less than a hospital as well, and the level of training of the aids that do most of the care is much lower.
Once again, that's not to say that there are better and worse ways of dealing with the situation. One home where I have 10 patients (out of about 120) had a few cases of Covid but little or no in facility spread, and has been Covid free for a month or more already. The other facility, only a little smaller, has had a slew of cases in staff and patients; indeed, both of my patients there got it. Surprisingly, neither got significantly ill at all, including one in her 90's who's been at death's door for several years! THAT'S actually what scares the pants off of us health care workers; while there are risk factors, you never know who is going to do fine with this thing, and who is going to be come severely ill and possibly die. The fact that so many people seem to get minimal symptoms of course makes it much harder to prevent it from spreading.