Brady: Hey there everyone, we're about to show you an interview with a mathematical biologist called Kit Yates.
It's about coronavirus. If you'd like to see a longer version, the full 28 minute podcast,
I'll put that on the Numberphile2
YouTube channel as I usually do and you can also listen to the podcast in all the usual ways. Just search for
Numberphile and it's the episode called "Gondor calls for aid"
Kit: So, my name's Kit Yates. I'm a
mathematical biologist. I'm also a senior lecturer at the University of Bath. And so by mathematical biologist,
I think people find that a bit of a strange one to deal with, because I think people think that
typically maths is quite pure and abstract, and biology is pretty messy in real world and never the twain shall meet. But umm
really what I do there today is take
biological systems that I think are interesting, so maybe anything from a swarm of locusts to the way that eggs get their partnering,
or the way that
Embryos develop; and try and write down a system of equations or computer code which describe that to try and make predictions about those systems.
Kit, you say that people don't often see the link between
biological systems and mathematics. I feel like that's changed pretty rapidly in the last few weeks.
Right, everyone is talking about exponential growth; about
epidemic;
epidemiological models; about
modeling and basic reproduction numbers, Boris Johnson was talking about the fast upward tick of the curve and
yeah, even Conor McGregor
I saw the other day was talking about implementing harsh measures to halt exponential growth of the disease in Ireland.
So yeah, everyone is err, everyone's talking about mathematical biology at the moment,
so it's a good time to be a mathematical biologist. - Is there a degree of that?
I know, I know I'm sure if you had a magic wand you would make this all go away and what a terrible thing
this is for the world. But are mathematicians kind of thinking "at last! People get it!" - I think that's true.
I think people, like there's, there's a good meme going around where it's just a guy standing a chalkboard drawing an exponential curve and
students saying "crap, when are we ever going to need this?"
Right and it's sort of the case. It sort of feels like, to some extent a little bit of vindication. Although, yeah, of course, um,
ideally you would wish it away if you could do, but yeah
I think mathematicians are trying to make the most of this opportunity and,
and to try and show people why maths really can be important. It can be a matter of life and death sometimes.
- Do you feel like
this has shown up, sort of a problem with
mathematical literacy? Or do you think people have kind of risen to the occasion
and they're getting it? Like how have you felt about how well the public are
understanding some of these things? Before we do start talking about the maths.
- Yeah I think, I think people are doing an okay job
actually. I think the fact that people are even talking about it and caring about, you know
how good these models are and asking these questions is a really good sign and
I think it's it's a little bit difficult to explain all the really complex models
that are out there at the moment, but I think that actually the basic mathematical models that underlie
epidemiological spread are actually not too difficult to understand in fairly, fairly straightforward terms
And I think it's our job as maths communicators to try and make those things as as understandable as possible
I think there's a lot of good people out there working really hard to do that.
- Coronavirus, Let's deal with that for a second. That's exponential growth?
- At the moment? Yeah. Like, so the way these, the simplest mathematical
epidemiological models work is you bake, you break the population down into three different compartments. They're called Susceptible,
so people who haven't had the disease,
Infected, so people who have the disease and can affect it other people, and then we have this removed category,
it's sort of a euphemistic term for people who have recovered - but also people that have died as well.
- This is the sir model we hear talked about? - Right this is, yeah
- We usually call it SIR but yeah, sir, whatever you want to call it really.
and
We, at the very early stages you have a whole bunch of people who are susceptible to the disease and very few people
who are infected and so
each individual can go and infect a certain number of people, who are susceptible;
we call this the basic reproduction number of the disease. And if that number of people that they infect
over the course of their infectious period is greater than one, then they will on average
infect that many people, who will then go infect that many people again, so
for Covid at the moment, estimates of the basic reproduction number are between 1.5 and 4, so
it's quite a big window.
But 2.5 is a generally sort of acceptable number.
So the first person goes and infects 2.5 other people they're going to infect
2.5 more, and 2.5 more and the, the exponential growth
then occurs. You get you start to see the numbers growing exponentially. - What kind of jobs are
mathematicians doing at the moment?
Like I can see what I can see the job of doctors and I can see that the job of researchers trying to come up
with vaccines. I mean,
the, these graphs and models you're talking about, they've been known long before
Covid came along and obviously they're being applied now.
But are their day-to-day things mathematicians can be doing? Like, new work they can be doing to help in this battle?
- Yeah, absolutely, cos every disease is different, right?
And these, these simple models that, that I've sort of described this SIR model, they can be made infinitely more complex, right
So SIR is fine for some very simple diseases,
but actually there's the extensions that we can make to those SIR models to include things like a carrier class,
so people who have the disease - but aren't
necessarily showing symptoms, so they're not necessarily umm
showing - you wouldn't class them as infected, cos you don't know they're infected yet,
but they've had this asymptomatic
period - which is what's happening with Covid. And so they can be spreading it without you even knowing that they're infected and that can be
that can be a real problem.
And it has been a real problem with Covid because, we can't just - isolate people as soon as they show symptoms,
we have to be isolating everyone in case they've got symptoms.
So, that's just one really simple extension you can make but adding in things like noise so stochasticity
or randomness, in the way that people bump into each other. Taking account of the networks with which people
interact with each other can make a huge difference as well.
You get these umm
people who are
social hubs, and therefore will spread the disease to lots of people compared to - people who are stuck at home and
don't go out so much so, you can make these things arbitrarily complex and there's actually been a call by the Royal Society for rapid
assistance in modelling pandemics. Where all
mathematicians, especially applied mathematicians, who have familiarity with modelling can sign up and help out in this cause so yeah,
there's loads to be done at the moment, and we're keeping really busy.
- Kit, how does someone
build in something like these, these you know,
these hub, super-spreader type people as opposed to people who are locked away? Like I see that they exist
but how would you put them into a model, these sort of unmeasurables? Or like, I see you could guess at what they are
but I, but then how do you? - So they're not necessarily
unmeasurables. We actually know a lot, a lot about our social structure, in part from using social networking data,
but also just, there's been a number of studies done and you can actually classify
the way that people interact using a network
so, people are noticing that network and they're connecting to the other people at, at edges.
And so you can classify
what's called the degree distribution of that network, which tells you how many people are there who have 100 contacts.
How many people with 99-98, and so on. Down to - how many people are there with no contacts? And that distribution
can tell you a great deal about the way that people interact so you can incorporate that network modelling into these SIR models.
So, you know, you start the disease off in a particular node with, you know,
a particular connectivity. How many people did they actually interact with? And you see how it spreads around the network.
So, they, they may seem almost intangible,
but, actually if we have good enough data -
and this is what it all comes down to really, if we have good enough data,
then we can actually capture,
capture these behaviours. But, data at the moment on this emerging pandemic is really difficult to come by.
- I mean
It seems pretty obvious that this pandemic's gonna leave a scar on the world and have some kind of, some kind of long lasting effect.
What about mathematically? Do you think it's gonna have a mathematical -
legacy? Is it gonna, like, because, because I've never seen mathematics being talked about so much with the global news of it.
- Yeah, exactly
I think, I hope, it will draw people into mathematics and make people realise that, you know, you
if you become a mathematician, you can have a real impact on the world. You're not just sat behind the desk
writing a textbook for, you know, for a subject which is dead and gone.
You're actually living in the real world, and you're doing things which can have a real
important impact on people's lives. So I hope that people,
future generations of kids who are studying maths in school at the moment will say "wow"
"This is actually this living, breathing, exciting subject and I want to be part of that"
And so I hope we'll get more people into mathematics.
And I also hope that people will take maths a little bit more seriously themselves,
so, maths generally only gets in the news when it's, you know,
the Fields Medal times and and, you know, people struggle to understand the very complicated maths that the Fields Medallists have done, the maths,
but actually,
you know, at the moment we can tell people about relatively straightforward mathematical models
which are having a huge impact on their everyday lives, And suggesting how we have come to this unprecedented
lockdown that we've never, you know, we've never seen before. So yeah, hopefully it'll have a really big impact on people's lives.
Just a reminder, the full 28 minute podcast
Numberphile2 - also numberphile.com or search Numberphile on your podcast player of choice
I'll also put some links in the video description to some useful videos and information
including the Numberphile video with Ben Sparks about the
Coronavirus curve and great ones from some other creators as well. And just a quick Numberphile update - before everything went into lockdown,
we actually did manage to film lots and lots of Numberphile videos, normal ones not Skype calls.
We're editing them at the moment and they'll be appearing in your feeds very soon.
Thanks very much for watching and I hope you are all staying really safe