And so I'm in Oxford this time and hopefully next term as well. But of course, I couldn't resist. There's a picture of the maths department in Cambridge on weather is always like that. So indeed my first slide, I have a plan for this tour. We're going to do five different topics. I'm going to get through quite a range of stuff, but I'm going to talk about the thing I know most about first, which is me.
You've already heard. My day job is. And Professor of mathematical biology professor as of this October. So I've just been promoted and the David and more fellow Queens College and this is the mathematical bridge in Queens College which some of you know very well. Yeah my research interests used to use master understand infectious disease and I have this obsession with flu in particular. So those of you who's actually studying maths at university or higher.
So quite a lot of you. So you know this fun when you meet someone new and they say, What is it you do? And sooner or later you're going to have to confess and say, I'm a mathematician. And, you know, there's a whole range of responses you get, right? Some of them good, some of them the good responses like, oh, maths, what bits of maths and will I understand it?
But that's the good response. And I'm always a little bit relieved because I can say I'm very, very applied maths so applied almost in biology. I did my Ph.D. I went to the Department of Zoology in Cambridge to do that and then came back to maths. And really I'm into infectious diseases. And then this poor person will then pause and go, Oh, I thought you said your maths, okay, you infectious disease. And then you can see them trying to piece together what it is you do. So you do epidemiology.
I said, Yeah, kind of. Kind of. That's a loaded word. Okay, so you do statistics. I can do some statistics, but you're imagining I'm going to count how many people die or something. That's not quite what I do. So then you can have a discussion and try and build up. So I'm going to try and take you through what usually happens in that thinking. So what people imagine I do as my thinking face. And sooner or later they realise I really am into viruses.
I'm interested how viruses evolve, how they interact with our immune system, different kinds of viruses. That's a cartoon of flu, which is, as you know, my favourite virus and not just viruses, but I think about the population dynamics and that's a plot of a few years of seasonal influenza in the UK. You get big years and small years and why it is now years, it's not always the same timing. So I think about these epidemiological patterns as well.
And of course I'm interested in how people move and how diseases mix both within one community and between. Do not recognise where I got this picture from. Excellent. I also love iPads games. It's this is plaguing this is how people. Well, actually, it's not bad. It's not bad game. So we get that. And then what do I do with that? So this is this is where it goes wrong. The imagination is that I have some big machine that I've built out of all these things and crazy model of everything.
And out of that machine pops a prediction, right? The answers 42. You realise by now? I realise this is not a very random audience. This is not what I do. But how do I explain what it is I actually do and what I'm going to try and give you in this talk is an insight into what we're actually up to, some of the research threads. I'm not just going to tell you one story, but I'm going to tell you a few different stories.
And eventually I will get to explaining why I'm wearing this t shirt and why Hazel is a very, very special place. So note no great sausage machine of models and easy answers. Well, why don't we do this? Actually, if we could, we would. But this is a nonsense. We can't do this. There's too much we don't know. You can't just put it all together. And if we did, it would be a complete work of science fiction.
It would be. We'd have something horribly wrong up here, and the whole thing would be a nonsense. So what I actually do these sort of things, maybe not as dramatic as predicting the next pandemic, but I'm hopefully going to show you how it is valuable in the fight against disease. Firstly, we build simple, simple, important, unusable models for not big monsters, but things we can actually do something with and gain some insights from.
Maybe this is the more obvious bit. We team up and work with experimentalists, so we may have a cycle of models where we come up with an idea and then design an experiment to test something. Use the model to explore the results and design the next experiment. We try and understand what happened in past epidemics. Quite often these will show Is this something really important we just don't know or have completely misunderstood.
And of course, we try to help identify what it is we need to know next. And maybe that's the less obvious thing. I'm going to talk mostly about this first thing and this third thing and hence slide this fourth thing. So that's all about me. That's all we need to know, basically. Bluff is guy to disease models. Actually, the biggest sections are section three and four. But I do want to tell you about this pandemic work. Bluff is going to disease models, right?
So next time you meet someone who says they do maths and disease, what you need to say to them, oh, do you do things like the asylum model? Right. And then you set them off in some interesting discussion. So just remember that bit who sort of the classic essay on model before. Oh, very non-random audience. Okay, I'm going to assume you haven't said everyone else. Right. Exile is an acronym susceptible, infected, recovered.
And in some sense, the simplest model of an epidemic needs people to be classified in exactly one of these three. And imagine this, everyone starts here. We're all susceptible to measles or this year's flu or something. Then, in fact, it's these people have been infected by someone else and they're now infectious and infecting. Pounded a whole bunch of stuff together, but we'll take that as one group and then are recovered, recovered with immunity.
Or die. The original essay, a formulation we all stood for removed, which is a little more ambiguous as to what happened to these people. As far as the math scores, they're just gone. So they're no longer able to infect anyone, nor can they get infected again. It's really about the dynamics coming through here. And there's only two processes in this thing, right? So you go infection and you've got recovery. That's it.
So beautiful. I'm going to show you the differential equations that represent this. So dsd, t d d t d r d t the rate of change of each of these three things. And as you might imagine, they add up to n, which is the total population size. Those of you who work within realise we've got some redundancy. So in fact we could throw away one equation here, but let's keep them all for clarity. So the transmission, the infection process goes in like this.
So you've got this Greek letter beta in France, which is controls how transmissible the diseases times are. Times s is so obvious why it should be only times this. So the number of people that get infected ought to be proportional to number of people available to be infected. Right. So this. And what right does each person get infected? Well, it depends how many other infectious people there are around. So it should depend on I as well.
So it starts to be intuitive and the fact that as a product we call it mass action. The recovery is even simpler. You go out of this class and into there, there's one recovery rate. So if this recovery rate is high, that means it's really short infection. If it's low or zero, it's a very, very long infection. And this models. Yeah, pretty much exactly 100 years old. His first written down and analysed. It's really simple, but it gives a lot of insights.
So typical output looks like this. So the blue dotted line, the number of susceptible people to it starts high and goes down. Basically it's going to think it can do in this more. Let's go down the red curve number of infected increases peaks and then decreases. This is time. Choose your favourite unit weeks, months, whatever.
And you get insights from this really quickly. Like if you look at the blue dotted curve, you see it's not going actually to zero, it's asymptote into some value other than zero, it's plateauing out. So this is one of the first things you learn from this model is epidemics end before they've got everyone. There's nothing special about these people escapes. They're just lucky. There will always be a few. And this is typical. This thing is over.
Nothing else is going to happen. And then you think, okay, this is how simple. This literally can't fit anything, surely. And the classic example we all like is this influenza epidemic. At a boarding school, it was a boys boarding school. So the access is a number of boys and it starts at 763. So the dots there, the data, if you like, the observe observed numbers. And the Cubs are the best for sale model. It's not perfect, but it's not bad for something with only two parameters, isn't it?
It's pretty good. Something different is happening at the end there obviously better at sort of ending the epidemic than predicted. But it's pretty good. This is a pretty bad epidemic because nearly everyone gets infected, but not literally everyone. So there we go. Surprisingly good model. You can gain a lot of insights from this. I'm going to pointedly not talk about our nought to the reproduction ratio, but you can look at that.
You can look at vaccine coverage that you need to achieve to protect against a particular disease. What I'm going to just point out what's wrong with this? Think about it for a minute. I'm not going to get you to share two answers in this, but think about what's missing from this. All I've got is this. I'll. Can you immediately think of four or five or six things that just say, I want to model the arrival of pandemic flu in the U.K.? Is this okay? No.
You were going. You had lots of things. Okay, here's my list. And of the lists intersect, intercept, lots missing, lots approximated. So one which I hinted at is this in fact, is an infectious being compounded. Of course, what actually happens is that you get infected by flu and you've got a day or two before you're really infectious to others. Maybe you can imagine how we can extend that. We just put another class in between E for exposed.
So you get susceptible, exposed and you're checking away and then you go into infectious. So we can fix that. There's no host demographics. This is the only thing that happens to our population. They just stay in recovered forever. Of course, there should be births and deaths which are nothing to do with the disease. Right. So newborns, my appearance susceptible and sort of tick through the system. And there should be natural death from every category.
I've talked about flu and measles, but many of the diseases we care about actually are really complicated with more than one phase. So HIV, for example, on first infection, you've got a burst of infectiousness for a few days and then there's a long time period until transition to AIDS. So you can't really just more or less say, oh, there's no recovery, but there's different levels of infected and how they're.
Spacial dynamics this Peter is is kind of saying every susceptible can contact every infected. It's like we're in one massive mixing bowl of everyone. Right. Actually, it worked ridiculously well for boys boarding school. Right. Kind of is a big mixing vessel, but for UK, that's maybe not a realistic model. Immunity is not always lifelong and perfect. You can lose immunity. Life. Oh, I also missed out the possibility you have immunity at birth as maternal immunity.
You have immunity from your mother for the first six months of life, and then that dies down. And then you have to build up your own life is random. This is a clockwork model. Essentially. The same thing will happen every time you run it. But stock activity matters, particularly when numbers are slow. So the time at which this thing takes off should be different. If I really run it, if I actually had a proper stochastic model, once it gets going, stochastic still less important.
Age structure. So we mentioned spatial structure as a way that people are structured, not all mixing together, but even if you deal with one town or even one school, it's not that all the kids are mixing equally, right? There'll be almost a mixing matrix describing how different groups are mixing with each other. And the special one in blue, which is the one I'm going to talk about virus evolution. This is about you have one infection, you recover and you stay immune to it forever.
This doesn't work for flu. There's more than one strain for something that strain means. Okay. So that was the bluff is going to say, oh, so now you know what to say to a disease model the next time you meet them, you know, it's pretty good. But the fun thing is if you meet someone working on this, which bit of extending okay, but if you're an expert ready to deal with strains, how do we cope with many strains?
So first, I'm going to show you why this is a really tricky problem and then I'm going to show you one way we've dealt with this and a little bit of my own work, but I'm also as well as giving you the results, I want to try and give you a sense of how this sort of fits into how do we get to actually dealing with infectious disease at the end of this? Is this just a mathematical exercise? And if I can do that, I'll be really happy. So quick crash course on influenza for mathematicians.
I'm interested in seasonal influenza. This is not pandemic influenza we're talking about. Yes, I'm interested in humans. Do you know what many other creatures get? Flu. I'm interested in humans here. Flu virus. It evolves. This is a phylogenetic tree of the H3 influenza type. It evolves to change how it appears. The immune system. Right. This is a cartoon, but it's these surface proteins actually look like caprese flakes or something.
They're actually they're far more complicated. Here's a bit of them. And what happens is it's these bits on the very surface of these proteins that stick out the change, which changes how our immune system sees it. So how I'd like you to imagine this is suppose we have one strain, we have immunity to it either because we've been infected with it and recovered and we've got a healthy immune system or because we've had the right vaccine for that strain.
But if you change the surface proteins, it's a bit like the influenza is basically disguised itself. It's not it's not literally like that. But as far as the immune system cares, it's not the same object anymore. Even though most of it's the same, the bit it first sees is not the same. And that's a really special property of flu that it can do this continual change. So this is what we'd like to be able to model. I can't just model is one strain.
But how do we do multiple strains? So you've got this idea, we've got this essay compartmental model. How do I turn that into a mini strain model? Okay, so let's just go for it's naive approach. Let's just extend the soil system, okay? Oh, but what does this mean now? Susceptible to which strain are infected with which strain are recovered from what?
And you think about this really start to realise we need actually lots of different S's and lots of different eyes and well actually we don't need the owners. The owners are just a special case of s, so you'd be susceptible to nothing and then you're kind of removed. So we need more than one s. More than one I. Okay. You ready to have a go at something? I said, no, let's try and do this between us. Okay. Let's imagine a disease with two strains and they've been imaginatively named one and two.
What are the classes that we need now? How many of them do we need? What are the classes now? How many of them do we need? So think about s classes. How many are we going to need? Maybe don't shout out, but have a think. So think it through. Okay. So we need someone. We need a class for people who are susceptible to both diseases. Yeah. So susceptible to one and two.
But then you need one for susceptible to strain one only susceptible to strain to only remember the special one susceptible to not one or two. Yeah. So actually, how many classes have we got now. Four. And I class is how many of those do we need. Matt's underground. So you can have a go at this one. Actually more than three. So you've got people who currently have stream one who previously had nothing. People who've currently got stream one. If previous you had stream two.
We don't worry about people who got strain on a previous health strain one because we say that can't happen, they've got immunity. So we chase that through. We've got four. Okay. That's not too bad for exes and for eyes. Actually, that's absolutely fine. We're going to look at that further. A much more troubling exercise, if I want to do flu evolution, to say something about which strain is going to become dominant at the end of the year, I might need to model about 100 strains.
How many categories do I need? Lots. Many, many, many more than I can do on a computer. Yeah, way more. So it's two to the power of 100, which is about ten to the power of 30. And it's really bad. It's huge. It's pretty more the number of particles of sand on earth or something and eyeglasses. Well, it actually goes like end two to the end minus one, which is even worse, actually.
So too many variables is the answer to that. I cannot take this naive approach and do a seasonal flu, which is bad astrology. I'm going to show you the sort of notation we use to do that. So we still use S and I, but we have to extend them a little bit. So the subscript here is previously had so many infections, we used a sort of set notation, so it s with one, two, three, four.
The category people have previously had strains one, two, three and four as one for previously and one of for you, this one. This is sort of a zero with a line through its empty set notation. So these are people who have previously had no infections. So this is the category we should be born into in some sense. Then we need some even worse notation for the eyes. So the superscript is the strain the currently infected with strange six, but they previously had one and three.
And we're going to assume you can't be infected with something you previously had, so you shouldn't have any six down here if you got six up there. So you keep this infection, history and subscripts, but your rates have been infected depends on the subscripts. So people in one who've had strains one and four, maybe they've got some immunity to strain to see modelled out in a slightly different way. You put parameters in to account for cross immunity when you've got it to your accounting rights.
I'm going to show a few slides with quite a lot of equations. Right. Some of you are going to absolutely love it because you're waiting for some equations. Some of you are going to get a bit twitchy. Please don't. What I'm going to do is tell you which bits I want you to look at and see. But I think I need to do this to show you what it is we actually do right outside the two strain model. One strain model.
It clearly is an essay already of showing you that a three strain model, only 20 equations and I can't fit that in a slide, so I have to do two. So firstly, what do we see? Well, let's start to take it apart. It's like this. I'll have my variables rate of change down here. I've got four S's and I've got my four eyes. And if you think about it, it kind of makes sense as a flow. So you starts, you've had nothing. We go this way, you have string one but previously had nothing recover.
Now you've had strain one previous you have strain one, got strain two and finally had both. We can go the other way and get strain two first and then just equations that are connected up in this way. You probably see a lot of terms are similar between the equations, right? So these ones with this Greek letter mu if I highlight those, those are all the terms to do with natural births and deaths. And you can see those one out is up here. So this is got a plus mu everything else is minus.
So the births are going in this everyone born in empty. So all the other terms. If it's not AMU, it's to do with the infection. A few other terms. The next most nice ones are these ones with the scanner in front. Actually, these are all to do with recovery. And this is the flow from eyes back to S's. Yeah. And that leaves these ones, which is where the action is. It's flows from essence to wise. It's infection happening. And maybe you can see a little bit of the asylum model in there.
It still beats at times. Okay. A combination of ice times and s maybe with the bonus factor in there crossed immunity, but it's still essentially in a soil type model. So this thing I've highlighted in Blue Beta Times, AI is something we call force of infection. It's the rate a single person will get infected if they're sitting in the system. It's sort of the pressure to to get infected from the rest of the system. And actually, we could just well, that's just a mess everywhere.
So let's give it a name. And we always use lambda or the capital lambda or lowercase. We like concrete letters. So lambda here, lambda one and two. And if I call that lambda one, call that lambda to, I can immediately make these look much, much less scary. Yeah. Better or worse? Bit better. Yeah. Still quite bad. So lambdas are these forces and these flows in between now. You can see these equations. Well, I still need these eyes in there.
I can't just throw these old equations out because they still appear everywhere. But there's one very neat move that someone had. You can write down the equations for lambda in themselves, but you can also get rid of them from the equations under a very neat move. I'm not going to go into the full horror of details of this, but this is the principal idea. This is the sort of system we've got at the moment. If we short circuit it like this.
It's a much more tractable model. I'm going to be like, hang on, where's the eyeglasses gone? Well, actually, the following this, they're still in the lambda. So what happens is now we flow between different classes of s, but it's no longer true compartmental models. It's not like you're in one of these or one of these. You're exactly in one of these. But you could also be in one of these. So you can sort of make an overlapping model.
So when you go from 0 to 1 because you've been infected by one, you're also going to be represented in here a little bit as well. So you're infectious with one. And this turns out to be a really good approximation for short infections. By short, I mean the infection is a small proportion of your lifetime. Yeah. So, flu, you're ill for five days. Lifetime, many years. So that's if you take the ratio of that, it's a small number. So this is really good or a modified model.
So actually what happens is you could speed through and get infected by both strains within a few days of each other, which can't happen here. You've got to wait there and then go there. Actually, we're quite happy to allow co-infection to happen for flu. It's possible. So it's already much nicer system now because this is now the full system. Six equations, eight down to six.
Does that impress you? Okay. But when I'm dealing with hundredths and order into to the end is now become order to to the end this this is a good step forward but it's still pretty sucky we can't really do to the end. So his his our bit of this what we thought that worked well how many of you PhD students. A few. Right. There's a little window when you know enough about your subjects to understand the background of what's happened.
But you don't know so much. Your mindset is stuck in a particular way. You have a little window of opportunity to do something really cool. And that's because you're silly enough to not know it shouldn't work. Enjoy that phase. I was silly enough. Oh, well, you know about that kind of trick work there, so I'll do it here. So these s variables, if I turn them into these theatres, so being an effective susceptibility rather than actually s is the same trick should work nicely.
So I can write these as theatres. Nice looking. Better and better if I can write some equations for defeated d t with that which don't need the s's. I'm done. Yeah. I'm going to spare you the details of this. But if I can do that and what goes in the question marks doesn't depend on any S's. I've got a closed system here. The bit on short circuiting is my PhD thesis. Right. I think it's not online and clearly it would take Cambridge servers down if I put it on.
You can get rid of the essays and write things simplified under some assumptions, some of them a bit technical, but it's related to how partial immunity works and how immunity accumulates. So if you get immunity from one strain and then another, how you combine those, if you will live with those assumptions, the system works. If the assumptions are not strictly true, and this is most of theses work, the system is still a good approximation to the full system.
So we can work with this reduced system most of the time. It looks like this is just we're just down to the features in the lambdas. Impressed yet. Oh, I'm surprised. You are impressed. We've gone from two to the N, which is a silly number, down to two. And so 100 strains is 200 variables, which is still quite bad, but I can put it in a computer at that point. Yeah, it's good news. So that's why it works.
So here's 100 strains with random cross immunity between them computes really large numbers of strains. I did that on a very old little laptop and no problem you can. Well, the point of it is you can now add other things. You see all these other complexities. We've made the strain bit easy. We can do other stuff with it. There's one figure I have to show you because it's the most expensive plot I have ever made. I don't have time to tell you that. But the story. Yeah. Here.
It is horrible, isn't it? It's terrible for many reasons. So the red colour here means zero. The red colour here means lots. Excuse a time, but the access disappeared and strain up the. But what it demonstrates is if you start it there, you tend to get clusters of strains. That's what it's supposed to show, the clusters of strains. It really doesn't need to be in colour. You agree? Do it in black and white. Perfectly well. I did it in colour.
I submitted it with the paper. And some of you know, that used to be a thing. And there still is a thing called page charges. And when journals were in print, they charged you a lot, lot more for colour. And this is the first paper I submitted on my own. Well, I've been in charge of it. My supervisor was co-author, I had no idea and a massive bill came through for these colour figures that were totally unnecessary.
Bear in mind, these are the days we'd have to put the colour figure on a CD and post it off somewhere and then you get a massive build up your own mind. That's, that's more than my annual rent. And I remember take it to my supervisor and it's the nearest he's been too angry with me. He's like, don't do that can. So we paid for it. So I'm going to enjoy this thick enough the rest of my career there is okay. We can model many strains. Julia gets a PhD thesis.
So what's really. What's the point of this? What's where does this go? Is this just a fun mathematical exercise? It was fun. But the. So what I want to try and communicate to you. All right. So there's the little bit of that paper dynamics and selection of many strain pathogens. But papers don't live this sort of isolated projects in their own right, the scientific threads to all of this. So we used many results and papers by other researchers and we cite those.
So that's a citation there. But also if you write a good paper and you get lucky, it goes on to be used by other people. This paper, she says, 250 other papers have used this. So it gets picked up and used by other researchers. And I'm going to show you the sort of thing this one has been used for. And they've picked these out slightly randomly, not very randomly. So this is another paper that cited this.
It's also quite a theoretical study, but looking at slightly more general situations as reinfection and vaccination. There's this paper about Lyme disease. I know nothing about Lyme disease, but turns out it's got strains as well. So it was useful. The strains are within the tick stage rather than the human stage. Malaria. And this is genetic Gupta's group here in zoology. Malaria has strains which are quite different to flu strains.
But some of the mathematics, some of the machinery can be reused between systems. HPV, human papillomavirus. This is a virus that can cause cervical cancer. So now it's routinely vaccinated against. But there are multiple types and again, strains. But this one. This is picked up by a research group in Cologne and used. Well, you know, I said we didn't do these bigger machine models. Actually, some people do. So they've got a model that's pulled together a lot of different things.
But the strain bit of it, how you do multiple strains, the epidemiological engine, if you like, is all thing. So that's a little bit of that study, right? Very, very cool because flu was thing in the end for me. And a way to understand then how this fits is. Here is a handy small cog I made. Right. I mean, other people really do have the larger machines. It gets used in larger machines. And that flu study I showed you, that team actually work for the last couple of years.
They've worked with the team that does the vaccine strain selection. So I cried when I had my vaccine because I'm a nurse. But it was a little bit of my research had helped with a little bit of the research, which helps choose the strain of vaccine in my arm. And that's really, really cool. It's a tiny bit, but this is a vaccine which goes to about half a billion people per year. So improving it just by Upsilon is worth it, making sure there's a better chance of making a good decision.
So hopefully that shows you a little bit about what we do. So crunching big equations done to smaller equations and then how it fits in. It's not us saving the universe, but it fits into other studies which will help improve something. Yeah. Cool. Pandemic time 2009. Influenza pandemic. Do you remember this thing? So I'm going to show you some data we've worked on from this.
This is a real pandemic. This is not a real pandemic. Okay. So, again, it's a big study with lots of us involved, and I'm giving you names. These are real people. We worked together. Actually, it's all us and UK. So actually I think there's only one American in that lot. So it's a very international team. The data we got was based on US medical insurance claims. So you might have opinions on different health care system systems.
One advantage is if someone goes to their doctor in the US, there has to be a medical insurance claim. Whether it's going to an insurance company or to Medicare, Medicaid, it has to be coded up. We have to know what the zip code is, the person who went in. We know how many of those visits were for influenza like illness. And the number of total visits where influenza like illness is what it says is the symptoms looked a bit like flu. There is no swabbing or lab test or sequencing.
There's just someone comes in with symptoms like cough and fever and feeling awful and it kind of looks like flu. It isn't always flu. You can probably see from that that you have these winter spikes, which are probably flu, but it never quite goes to zero in the summer, whereas flu literally goes to zero in the summer. So some of that is allergies, other non-infectious things, plus other viruses.
So you've got this baseline which is probably generally sinusoidal, which is in here sinusoidal and the excess is free. But a signal in that in 2009, this is what things look like in the US. So January to April or so you have the normal seasonal flu of the flus that were circulating at time. At that time here we have a spring wave actually UK. We had much more of a spring way of things much earlier, much earlier. And what you'll see is this wasn't all of the US as any bits of the US got this.
And then there was this monster in the autumn and the autumn wave. The full wave, I should call it. Really. I guess I'm going to show you a movie of this just of the 2009. These are the different places you recognise. This is the US. The size of the circle is proportional to the population there, so the area is proportional to population size colour. I'm getting better with my colour. So green is literally nothing.
And then it goes through to a sort of blue and purple for loads and we're going to start at beginning of 2009. Remember, this is seasonal. This is spring wave. That's autumn wave. So seasonal. Spring wave. And here comes. The Autumn wave. I really could watch this all day, but I won't. You see, the seasonal bit does have. Make it once again. Just once more. It has some patterns. You got a little blip of panic where everyone just has a little panic.
Go to the doctor because Mexican swine flu is here, I guess. And then you actually have a real spring wave in the northeast in Chicago. Then the fall wave sort of starts around here. Except for California, which does the same thing. And it takes weeks and weeks and weeks to get across the US. I mean, you could walk across the US in that time. It's really slow. So what's going on? And this is where we need models and maths again. So you've got this datasets.
Higa Can you now tell me, were schools important in spreading this disease? Now you've got to dissect it using some math. So that's part of our role. So first thing we want to do is for each place, say, when the autumn wave arrived and here's the Time series for individual places, it's pretty noisy. But for each place, we've got a way of looking at the full dataset and saying that's when it switched from being baseline to pandemic is here.
And I've brushed away someone's weeks worth of work to come up with a nice method of doing that. So there's a bunch of statistics behind this deciding how you do that nicely. You trust we've done that kind of okay. But you can see there's some ambiguities. You can then colour code places. So green ones start really early yellow the next wave. So the colours are now the time of arrival. And you can see it's a beautiful rainbow like thing.
But beautiful in some sense. And they really are different. So here's the curve for Atlanta City down here and here's for Boston City B in blue. And they really are separate by ages. It wasn't as if people weren't flying between the two every day. They were as carefully showing you the east only right. The rest of the US is complicated and it's not. There's no one there. There's just not enough that we can really say on sets for sure, for pretty small population sizes.
And you see, California is just its own thing. So you can do statistics like say correlate onset time with school opening because this is happening over August, September or October and schools in the US go back at different times depending on which state you're in. So the southern states go back earlier and the northern states go back later. And you know what? The onset correlates beautifully with school opening.
But before you're too quick to blame the schools, there's the diagonal, as it were. And you can see, yes, it correlates, but it's not quite explained by schools open. And then influenza hits a week later. Schools open and influenza hits a month later. So it's not quite the whole story. In fact, you can get as good a correlation just by looking at great circle distance. I haven't said where from. But zero is a place called both in Alabama.
It's the first place that popped up. I used to ask and talk to anyone ever been there? And then someone said Yes, one day I'm going to do that again. There was a lot of talk at the time. Is climate and weather being important? Do you know what this thing correlates with? Humidity as well. As you increase absolute humidity, the onset date becomes earlier. I'll separate at eight Eastern movies. But all of these all of these correlations I've shown you are ridiculously significant.
So you get this phase of panic of the pandemic. Oh, yes. It's all about schools. It's all about humidity. It's pure geographic. And then you start to suspect your colleagues have lost the plot. Really? And you have to show them a really silly correlation to get in, to get over it. So silly correlation here. You want something that correlates with this. It's different in the south and the northeast, right? So you come up with some suitable quantity and you correlate it.
It's just this is Obama is the nearest time. And you know what? It's beautiful. And you can see this bit of your colleagues trying to say for a moment, well, then, you know, Republican voting did. No, it didn't. It's just everything correlates. There's a spatial pattern, right? Any spatial pattern in correlated with anything you like. And you can have fun submitting papers under the names of your enemies for these.
So which factors actually matter? Right. If you want want to take this apart, you can't just do it by correlations. You really need to construct a spatial model. And this is sort of stuff you do. Then build a model and disentangle it and try and see what matters. So going to make model where we include humidity, don't include humidity, see if it's okay with or without, see what matters.
And the force infection between cities. It's force of infection against the same thing, sort of a rate or pressure of getting infected. But rather than thinking about individual people now, think about cities. Yeah. So red city here is infected pandemics well and truly taken off there. This place is not. And I want to know the sort of probability per unit time, per week, per day of infection, jumping from here to here.
Then you put in every factor that everyone suggested is importance, not voting patterns we didn't put in might depend on population size, and each place might depend on where the schools have started in the target place, humidity in the target place, and of course, the distance between them, whether people can actually travel between them easily or whether they're just opposite ends of the country.
You throw it all in and give me the schematic idea here, which is we've got a probabilistic model now. It's it's no longer deterministic. It's probably stochastic. So I think we need to run it a lot of times. So we need to do some clever stuff with likelihoods. We've got these observations here. Here's what actually happened in 2009. Once, what's the chances of observing this thing given this model?
So for each one of our models and we've got a lot of models, you then change your parameters here to make this as likely as possible to fit its maximum likelihood style to this thing. Right? Is that okay? So for each model, I'm making the best one. Then you make lots of models and this doesn't look like the worst line, but I think this is conceptually the worst slide because each of these rows represents a class of models.
Actually, within each one there's many dozens of models. I'm going to pick the best one. Do they include local transmission? Do they include schools been on or off? Do they include humidity? And for each model, we can come up with a quantitative score of how good it is, as in how well does it fit and how parsimonious is it? Does it include loads of crap which does nothing as well. So comparison to observed data and I've turned that numerical score into terrible.
Okay. And good, which is pretty much what it does anyway. And these are the eight possibilities of mixing these three on and off. You can see the first four. If you don't include local transmission, the fit is terrible. It will always be terrible. That should have been obvious to you from the movie. The you could see is like a wave, right? So the ones that do include it are basically all at least. Okay, all good. Can you see what factor is next?
Most important there. Yeah. So the two with schools not been considered okay. The two with them are pretty good. So it's better to include them and humidity. It doesn't really do anything by the time you've accounted for everything else. Humidity doesn't add anything. So in parsimony we say, okay, it's a non-issue. Humidity was not important, at least for the onset of pandemic, and 2009 may have been important for how severe infections were.
But in terms of arrival, some of you would like to actually see the model, right? Okay. It's a lambda is a force of infection. We just throw lots of stuff in this humidity. There's weather. There was a spring wave. External seating indicator functions for schools in each place, population sizes, a distance function and this fun normalisation thing. And then you can build up a likelihood model from there.
I can give you a summary of these results, but I'm going to tell you why you should be suspicious of these models as well. We found, of course, it was strong short range transmission. Nearby cities infected each other. You got occasional long range or even international transmission. California was a jump. It had just clearly come over internationally or the whole way across the country at the time. Schools, yeah, slightly important, but not very humidity.
No, population size is slightly, but that's a tricky one because the cities are sort of normalised in some sense already. But let's have a little think about this. One city infecting another actually means and why you should be a little troubled by this. So again, the models we build aren't necessarily all the models in the world, it's the ones that we think of. And that's very much shaped by our understanding of how things work. So trial models shaped by current knowledge us is tricky.
So let's do something closer to home, right? And choose two cities at random. Let's call them out and see. This is my commute each week. If only there was a road which went like the arrow. So I'm talking about Oxford infecting Cambridge. What crazy world is this? This is like some giant sneeze from Oxford to Cambridge. I mean, that's I was going to say that's silly, but I actually have an office mate, so once upon a time you probably could sneeze that far.
This is clearly not happens and not what happens at all. And what we're doing by thinking about this, thinking about cities is right. But underlying it, of course, is a much more detailed model. So maybe let's suppose a pandemic is hit, some people are infected and not everyone and no one say infection. How does it get between the cities without massive sneeze? See me can't sneeze at four. I could think of three ways. Yeah. Maybe you've thought of one.
Maybe you just thought of the second. I wonder which ones. So first one is maybe someone who's ill in Oxford, goes to Cambridge, looks around for a day, goes back and someone gets ill. Right. So an infected can travel to the other city. That's one way of doing it. Not the only way. Can you. Can you now think of another way? So it's this reset that. Yeah, exactly. Other way. So someone who's susceptible in Cambridge like me comes and hangs out in Oxford for a while and captures of someone,
takes it back and goes and affects all of Cambridge. That's another way. Can you think of a third way of doing this? Yes, I saw some of that. Yeah, of course. You can have someone. There's a third party city that people go to. Infection happens and yeah. Go home, infect everyone. So I've somehow fudged. And this is this is a more realistic model, still bonkers.
But to get this right, I'd need to know how everyone in Oxford and Cambridge moves where they go, where they hang out, where they spend their time and build a massive model out of that. And you can see we're very quickly into London, complete bonkers, right? Cause we can't do this. What we do instead is think of it in a far simpler way. And just so there's a probability of people infection getting from here to here by one of those three means,
and it depends on the distance between the towns. So it tells of exponential models what we typically use because it fits jolly well. You could see, you know, we don't literally believe this is true, but it's simple to work with. It's good enough. You can also check how robust things are because we can change this a bit. We can pull it in a bit tighter, a bit looser, and see if our main results don't change.
Then it didn't matter. We didn't put those complications in. But if they do, then we better know a little bit more about how this actually works. So do we actually know what we're missing? And last 5 minutes, that brings me perfectly on to explain why I'm wearing this crazy t shirt, screwing around with the picture of Hannah Fry on my tummy. Go the BBC pandemic. This is not real pandemic, but. But it's a virtual pandemic. We have a mobile phone app. Has anyone done this?
Oh, new people. All right, so we actually members BBC pandemic. But you can go and get it on the website. We can go to the Apple store or your Android store and just search with BBC pandemic and run this thing. If you're happy with what it does after I've described it, it's this is going to be part of a TV programme. It's going to be probably a 90 minute programme on BBC four early in 2018, which you'll notice is the centenary of the big flu pandemic.
But it's also a really big citizen science project. Real data is being collected. We are looking at anonymizing it and then we're going to make it available to the scientific community to help inform many other studies, not just about the work, but these other machines as well. Right. And the key components to this, the big study is the national one. Right. This is the one you can take part in. It's still running now.
So the collection is once you agree to do this, you need to be 13 or over to do this. Otherwise, I'm afraid we have to throw away your data collection. Period is 24 hours and when you press go it record once per hour where you are down to square kilometre. So it's not super creepy. It doesn't follow you around the house or something, it just knows which square kilometre you're in.
And some square kilometre mesh is a short survey at the start where you say, Answer a few questions about yourself and there's a contact survey at the end, which is how many people did you actually interact with over the last 24 hours? Tell us a little bit about them. Was the context work or school or home? And you can do more than one day if you like, but doing at least one day would be really useful to us.
So if you're happy with this and one kilometre every hour is not particularly intrusive, please go and do it. We need as many people as possible and a diverse group as possible to do this. Don't even worry about which day you're doing. Just choose any random day. It was a day that's boring and you're at home. That's fine. We need to understand what typical pictures are like as well. That's a national. But what about Heysel myth? Why does the country need Heysel?
May Well, this has already happened, actually, I have to confess. So this was much more intrusive. It was collection period of three days. The recordings were as frequent as a mobile phone would do without emptying its batteries completely. It tended to be every few seconds. Okay. And as accurately as chips would allow, which meant in some cases it really was filling around the house. And here's a little zoom in of Haslemere. We have a uniquely detailed study of one towns.
We know what an epidemic in this community would look like in great detail because we know how people move. We've done it. I can't tell you what happened. You got to watch the programme, but it worked. I'll tell you that much just to show you there are mathematicians behind. This is also we've got a team of four of us who are during the number. Working behind the scenes for Petra. Stephen Maria a must see.
I got my thinking face again. This is us actually in hazmat ready for the filming for the big reveal at the end. And this is what our Sunday a few weeks looked like. 1 a.m. The collection was Thursday, Friday, Saturday. They closed it Saturday night at midnight and we get the date file, I think it is 1:10 a.m. on a Sunday forum. We finished running the simulations of the hazelnut epidemic. There's some work to be done tidying up with data and then running it and then verifying it.
And the longer we work into the night, the more we have to recheck things. We don't trust what we're doing anymore. We actually finished for him, which is earlier than we'd hoped. 10 a.m. we went to Hazmat 2 p.m. I don't quite notice I was going to be stuck on camera that day. So if you watch the programme and I'm like, I have bad luck on that day, you forgive me, that's what happened. That's those in Hazmat beforehand.
And of course we were thinking of the people as the dots because we saw the dots moving around on the screen, all these dots going over there. And that's I was going, oh, my goodness, the dots are here. There were you actually people I can't tell you the results, but they're pretty cool. But why mislead to both the Hazel Wear study, which is really detailed and quite big, and the national study which is already monster big and I hope more people do it.
So we might be able to answer things like how far do people actually move on a typical day on average, I'm not talking about air travel, I'm talking about normal day to day movement. How does it vary by age group. We could probably all sit down and try and imagine how that is, but do we know for sure? And from what we've seen already, our assumptions don't work. Here's here's a fun one. Do people in larger cities move more or less than people are in more rural areas?
You sort of think of cities as movement and rural. You stay in that same place while fishing of the US. Data suggests that the reverse is true, but we can't actually find any data to verify that. But we should be able to. From here we can look at people living in these postcodes and not very dense to see they move more than people who are living in inner city postcodes. There's a week. How a Saturday is different Wednesdays do people move?
More or less? What do you think? I don't know the answer to that, but hopefully we can put the answer in the TV programme we get there. So there it is. So hopefully we can answer some of that with the BBC pandemic data. But this talk is also about the scientific threat. And just to wrap up, this isn't going to save the world in its own right. We're going to pick it up and hype it.
But of course, what we're producing and this will go to the scientific community in the end is another small cog, very valuable because it has been no study of this scale before done with mobile phone tracking of this kind and certainly not nothing like it. In the UK there'll be some research papers and I'm into flu, but they won't all be flu. There'll be something else. Maybe there'll be for the diseases that we don't know the names of yet. They haven't arrived yet.
Maybe this data here will help us better understand how people move in the UK so the next round of control measures might be a bit better as a result. We don't know what, but we feed into the scientific threat and hope it will be picked up by others. Our job is to communicate what we know about this data and to share it with others. So that brings me to the end. We've we've got to the end of the plan and we've got through a lot of different topics.
But hopefully I've given you a sense of what it is we actually do and using maths to study infectious disease and how broad it is. Thank you all very much for coming tonight and thanks for listening.