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?