Feeding My Ignorance

One thing that I used to dread when I was working was someone asking me "what do you do at work then"?  I suspect that I must have written about this somewhere, but the answer "I do modelling" is perhaps the most accurate and yet least informative one that I could give.  Suddenly "modelling" is becoming quite the in-thing.

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As we dive deeper into the covid-19 crisis it transpires that governments (and presumably others) everywhere are using models to track, understand and predict the unfolding situation - and all of a sudden "modelling" is beginning to be understood by more people - well, I say understood, but one of the BIG problems with any modelling is its much easier to misunderstand than to understand.

A couple of years ago I wrote about data representation/misrepresentation - and this is a pertinent time to go back to some of that.  I guess the best place to start is with my penultimate paragraph then which warned that anyone presenting the output of a model must be very mindful that "what you thought you said is not what the other person thinks she heard!" There are a number of subtleties in that!

One of the strengths of modelling is also potentially a huge weakness - you get numbers out the end.  This helps.  Unfortunately it also means that people start believing the numbers without having a clue about what assumptions were made using the models.  There was a great example of modelling last week in the Washington Post (sorry for providing a link to a site that has only limited accessibility!) which brilliantly illustrated the effectiveness of social distancing.

The problem is that presenting such good output to a relatively uninformed audience can convey too much information.  Yes - the model showed that restricting movement reduced the number of contacts which could potentially result in spreading the virus and therefore reducing the death toll.  However, it was, I suspect, a very simplistic model - and note that is NOT a criticism, the more simple the model the better in most cases, but it goes hand in hand with some huge assumptions.

As a model gets more "realistic" it also gets (usually) more complex.  I don't know how the model that was reported in the Washington Post works, so I shall instead describe a fictional model that I am creating here for myself to show the same sort of interaction.

At its most basic assume there is a population of 1000 people.  Each person spends a percentage of their day interacting with others - say 40%.  For the purposes of the model the interaction space is tiny - so everyone who is interacting at any time will inevitably encounter a proportion of the others - say 50%.  Of those with whom you interact - a percentage will be infected.  An interaction with an infected person will result in you becoming infected  with a probability that is non-zero.  This probability measures the level of contagion of the disease.

Of those who are infected a sizable percentage - say 10% - will become very sick and therefore load the health service.  A smaller percentage of those will die.  All those who do not die will recover and be immune - those who are hospitalised will take longer to recover than those with mild symptoms.

We could now run this simulation to see the pattern of infection and, like the Washington Post model re-run it with fewer of the whole population mixing and interacting - we would see quite different patterns of infection.

As a "first pass" model this would be adequate to demonstrate that limiting the mobility of the population slows the spread of the disease - much as the Washington Post model did.  Lets look though at the limitations of this model and do a little bit of development to illustrate how quickly this type of model would get complex and much more difficult to understand - and therefore provide results that are more difficult to interpret.

This first thing that could be looked at is the geographical nature of the interactions - people interact in different situations - each of which has different levels on interaction - the chances of infection are (I imagine) much higher if you share an elevator with someone than if you pass in the park.  I can only assume that the two meter social distancing rule is based on some solid science, so any interactions that do not bring you closer would be ruled out completely - presumably there is also less chance of infection at one meter distance than if you are touching the other person.

(note : the two meter rule is a good one for public advice - it is not sufficiently clear as a modelling parameter though - infection risk is almost certainly a function of distance apart)

What else forms part of that function?  There may be times in the cycle when the virus is more transmittable from one to another; there are almost certainly ways in which the virus can be transmitted without getting closer than two meters - say on the handle of a door; just how contagious is the virus anyway.

and many more....

According to one set of figures I heard on average everyone infects two other people - making it a bit more contagious than the flu.  Who knows whether that is right or not.

Anyway - the title of this blog is feeding my ignorance and so far on this post I have been more demonstrating my knowledge (such as it is).  Thing is - although I know plenty about how to model and I can very quickly point to flaws or holes in existing models - I do not have the knowledge to build a decent model myself.  What I can do - and what everyone ought to do to a certain extent - is to remain open-minded, calm and clear headed.  If the model says something scary - there are almost always mitigating factors.

One of them is that the numbers are being 'presented' in such a way that they are designed to scare people a bit.  The big issue in this is probably time - given enough time the vaccines will be available - albeit too late for some.  If each case is treated sequentially then the health services will cope - if they all come in the same week the health services will be overwhelmed and many will die who could have been saved.  The actuality will be somewhere in between - and the "flatten the curve" message is a useful catchphrase to describe what needs to be done.  Even a little flattening will help - but the flatter it can become the more the death toll will subside - although that in itself is an oversimplification.

Those responsible for decision making are trying hard to ensure that enough people are sufficiently worried to sit on their sofa - which is the equivalent of sitting on the summit of that curve - pressing it down by simultaneously reducing the number of people who can be infected (the population running around outside) and ensuring that the number of severe cases remains at a reasonable ratio to the number of ICU beds.

So yes - this has "fed my ignorance" as I wanted to understand a bit better the thinking behind the "stay at home" advice.  Its not because Covid-19 is particularly dangerous in itself so much as it is dangerous because it is new and so many people are susceptible to it.

Might try to build my own model - not too come up with answers - but to understand the other things that impact here.  The more comprehensive the model, the more complex it becomes and the more difficult it becomes to interpret the results - but without that complexity there are going to be so many unintended consequences that any positive impact of the modelling would be swamped by the negative.

In the words of a very famous quote from George Box :

All models are wrong, some are useful

p.s. please note that the quote requires careful understanding in itself - it is itself a model, is useful - and wrong (certainly if misinterpreted)