1 00:00:12,060 --> 00:00:15,810 And so I'm in Oxford this time and hopefully next term as well. 2 00:00:15,840 --> 00:00:23,460 But of course, I couldn't resist. There's a picture of the maths department in Cambridge on weather is always like that. 3 00:00:25,710 --> 00:00:29,240 So indeed my first slide, I have a plan for this tour. 4 00:00:29,250 --> 00:00:30,930 We're going to do five different topics. 5 00:00:32,020 --> 00:00:38,910 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. 6 00:00:41,310 --> 00:00:46,889 You've already heard. My day job is. And Professor of mathematical biology professor as of this October. 7 00:00:46,890 --> 00:00:51,810 So I've just been promoted and the David and more fellow Queens College and this 8 00:00:51,810 --> 00:00:54,870 is the mathematical bridge in Queens College which some of you know very well. 9 00:00:57,300 --> 00:01:03,990 Yeah my research interests used to use master understand infectious disease and I have this obsession with flu in particular. 10 00:01:05,340 --> 00:01:11,970 So those of you who's actually studying maths at university or higher. 11 00:01:12,840 --> 00:01:17,730 So quite a lot of you. So you know this fun when you meet someone new and they say, What is it you do? 12 00:01:19,020 --> 00:01:22,500 And sooner or later you're going to have to confess and say, I'm a mathematician. 13 00:01:23,250 --> 00:01:25,799 And, you know, there's a whole range of responses you get, right? 14 00:01:25,800 --> 00:01:34,950 Some of them good, some of them the good responses like, oh, maths, what bits of maths and will I understand it? 15 00:01:34,980 --> 00:01:43,139 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. 16 00:01:43,140 --> 00:01:48,300 I did my Ph.D. I went to the Department of Zoology in Cambridge to do that and then came back to maths. 17 00:01:49,680 --> 00:01:52,630 And really I'm into infectious diseases. 18 00:01:53,460 --> 00:02:01,260 And then this poor person will then pause and go, Oh, I thought you said your maths, okay, you infectious disease. 19 00:02:01,590 --> 00:02:06,610 And then you can see them trying to piece together what it is you do. So you do epidemiology. 20 00:02:06,630 --> 00:02:11,160 I said, Yeah, kind of. Kind of. That's a loaded word. Okay, so you do statistics. 21 00:02:12,360 --> 00:02:17,610 I can do some statistics, but you're imagining I'm going to count how many people die or something. 22 00:02:17,670 --> 00:02:21,990 That's not quite what I do. So then you can have a discussion and try and build up. 23 00:02:22,020 --> 00:02:25,680 So I'm going to try and take you through what usually happens in that thinking. 24 00:02:26,160 --> 00:02:30,570 So what people imagine I do as my thinking face. 25 00:02:33,690 --> 00:02:36,570 And sooner or later they realise I really am into viruses. 26 00:02:36,580 --> 00:02:43,170 I'm interested how viruses evolve, how they interact with our immune system, different kinds of viruses. 27 00:02:43,320 --> 00:02:49,020 That's a cartoon of flu, which is, as you know, my favourite virus and not just viruses, 28 00:02:49,020 --> 00:02:56,730 but I think about the population dynamics and that's a plot of a few years of seasonal influenza in the UK. 29 00:02:57,200 --> 00:03:01,710 You get big years and small years and why it is now years, it's not always the same timing. 30 00:03:02,190 --> 00:03:05,430 So I think about these epidemiological patterns as well. 31 00:03:06,450 --> 00:03:13,290 And of course I'm interested in how people move and how diseases mix both within one community and between. 32 00:03:13,350 --> 00:03:16,860 Do not recognise where I got this picture from. Excellent. 33 00:03:17,190 --> 00:03:22,740 I also love iPads games. It's this is plaguing this is how people. 34 00:03:23,010 --> 00:03:27,180 Well, actually, it's not bad. It's not bad game. So we get that. 35 00:03:27,180 --> 00:03:31,470 And then what do I do with that? So this is this is where it goes wrong. 36 00:03:32,830 --> 00:03:39,900 The imagination is that I have some big machine that I've built out of all these things and crazy model of everything. 37 00:03:41,970 --> 00:03:45,600 And out of that machine pops a prediction, right? 38 00:03:45,600 --> 00:03:54,250 The answers 42. You realise by now? 39 00:03:54,580 --> 00:03:57,520 I realise this is not a very random audience. This is not what I do. 40 00:03:58,720 --> 00:04:04,959 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, 41 00:04:04,960 --> 00:04:09,640 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. 42 00:04:09,970 --> 00:04:16,840 And eventually I will get to explaining why I'm wearing this t shirt and why Hazel is a very, very special place. 43 00:04:18,850 --> 00:04:23,830 So note no great sausage machine of models and easy answers. 44 00:04:24,250 --> 00:04:27,940 Well, why don't we do this? Actually, if we could, we would. But this is a nonsense. 45 00:04:27,940 --> 00:04:31,690 We can't do this. There's too much we don't know. You can't just put it all together. 46 00:04:31,690 --> 00:04:34,780 And if we did, it would be a complete work of science fiction. 47 00:04:34,780 --> 00:04:39,250 It would be. We'd have something horribly wrong up here, and the whole thing would be a nonsense. 48 00:04:39,940 --> 00:04:47,139 So what I actually do these sort of things, maybe not as dramatic as predicting the next pandemic, 49 00:04:47,140 --> 00:04:50,260 but I'm hopefully going to show you how it is valuable in the fight against disease. 50 00:04:50,920 --> 00:04:56,920 Firstly, we build simple, simple, important, unusable models for not big monsters, 51 00:04:56,920 --> 00:04:59,980 but things we can actually do something with and gain some insights from. 52 00:05:01,300 --> 00:05:04,810 Maybe this is the more obvious bit. We team up and work with experimentalists, 53 00:05:04,810 --> 00:05:09,940 so we may have a cycle of models where we come up with an idea and then design an experiment to test something. 54 00:05:10,270 --> 00:05:18,520 Use the model to explore the results and design the next experiment. We try and understand what happened in past epidemics. 55 00:05:19,240 --> 00:05:23,860 Quite often these will show Is this something really important we just don't know or have completely misunderstood. 56 00:05:25,300 --> 00:05:30,370 And of course, we try to help identify what it is we need to know next. 57 00:05:30,370 --> 00:05:37,630 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. 58 00:05:38,980 --> 00:05:42,580 So that's all about me. That's all we need to know, basically. 59 00:05:45,350 --> 00:05:51,020 Bluff is guy to disease models. Actually, the biggest sections are section three and four. 60 00:05:51,470 --> 00:05:56,140 But I do want to tell you about this pandemic work. Bluff is going to disease models, right? 61 00:05:56,150 --> 00:06:03,530 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? 62 00:06:04,190 --> 00:06:11,420 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. 63 00:06:12,650 --> 00:06:17,180 Oh, very non-random audience. Okay, I'm going to assume you haven't said everyone else. 64 00:06:17,180 --> 00:06:23,330 Right. Exile is an acronym susceptible, infected, recovered. 65 00:06:23,810 --> 00:06:29,150 And in some sense, the simplest model of an epidemic needs people to be classified in exactly one of these three. 66 00:06:30,020 --> 00:06:37,010 And imagine this, everyone starts here. We're all susceptible to measles or this year's flu or something. 67 00:06:37,880 --> 00:06:44,000 Then, in fact, it's these people have been infected by someone else and they're now infectious and infecting. 68 00:06:45,580 --> 00:06:52,750 Pounded a whole bunch of stuff together, but we'll take that as one group and then are recovered, recovered with immunity. 69 00:06:53,830 --> 00:07:02,690 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. 70 00:07:03,700 --> 00:07:09,670 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. 71 00:07:10,840 --> 00:07:15,830 It's really about the dynamics coming through here. And there's only two processes in this thing, right? 72 00:07:16,420 --> 00:07:20,170 So you go infection and you've got recovery. That's it. 73 00:07:20,170 --> 00:07:25,300 So beautiful. I'm going to show you the differential equations that represent this. 74 00:07:27,040 --> 00:07:32,380 So dsd, t d d t d r d t the rate of change of each of these three things. 75 00:07:32,860 --> 00:07:36,700 And as you might imagine, they add up to n, which is the total population size. 76 00:07:37,540 --> 00:07:43,900 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. 77 00:07:45,820 --> 00:07:49,930 So the transmission, the infection process goes in like this. 78 00:07:50,620 --> 00:07:57,310 So you've got this Greek letter beta in France, which is controls how transmissible the diseases times are. 79 00:07:57,370 --> 00:08:00,190 Times s is so obvious why it should be only times this. 80 00:08:03,070 --> 00:08:08,440 So the number of people that get infected ought to be proportional to number of people available to be infected. 81 00:08:08,440 --> 00:08:13,270 Right. So this. And what right does each person get infected? 82 00:08:13,300 --> 00:08:17,300 Well, it depends how many other infectious people there are around. So it should depend on I as well. 83 00:08:17,920 --> 00:08:22,510 So it starts to be intuitive and the fact that as a product we call it mass action. 84 00:08:23,740 --> 00:08:29,229 The recovery is even simpler. You go out of this class and into there, there's one recovery rate. 85 00:08:29,230 --> 00:08:33,160 So if this recovery rate is high, that means it's really short infection. 86 00:08:33,490 --> 00:08:37,060 If it's low or zero, it's a very, very long infection. 87 00:08:38,930 --> 00:08:43,070 And this models. Yeah, pretty much exactly 100 years old. 88 00:08:43,340 --> 00:08:49,040 His first written down and analysed. It's really simple, but it gives a lot of insights. 89 00:08:49,070 --> 00:08:56,600 So typical output looks like this. So the blue dotted line, the number of susceptible people to it starts high and goes down. 90 00:08:56,720 --> 00:09:04,700 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. 91 00:09:05,150 --> 00:09:08,720 This is time. Choose your favourite unit weeks, months, whatever. 92 00:09:09,890 --> 00:09:16,370 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, 93 00:09:17,960 --> 00:09:22,310 it's asymptote into some value other than zero, it's plateauing out. 94 00:09:22,790 --> 00:09:26,870 So this is one of the first things you learn from this model is epidemics end before they've got everyone. 95 00:09:27,740 --> 00:09:30,740 There's nothing special about these people escapes. They're just lucky. 96 00:09:31,130 --> 00:09:34,570 There will always be a few. And this is typical. This thing is over. 97 00:09:34,580 --> 00:09:39,920 Nothing else is going to happen. And then you think, okay, this is how simple. 98 00:09:39,920 --> 00:09:46,790 This literally can't fit anything, surely. And the classic example we all like is this influenza epidemic. 99 00:09:47,540 --> 00:09:54,350 At a boarding school, it was a boys boarding school. So the access is a number of boys and it starts at 763. 100 00:09:55,850 --> 00:09:59,750 So the dots there, the data, if you like, the observe observed numbers. 101 00:10:01,320 --> 00:10:09,010 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? 102 00:10:10,990 --> 00:10:15,970 It's pretty good. Something different is happening at the end there obviously better at sort of ending the epidemic than predicted. 103 00:10:17,220 --> 00:10:23,730 But it's pretty good. This is a pretty bad epidemic because nearly everyone gets infected, but not literally everyone. 104 00:10:25,700 --> 00:10:29,690 So there we go. Surprisingly good model. 105 00:10:29,780 --> 00:10:36,679 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. 106 00:10:36,680 --> 00:10:43,610 You can look at vaccine coverage that you need to achieve to protect against a particular disease. 107 00:10:44,660 --> 00:10:48,440 What I'm going to just point out what's wrong with this? Think about it for a minute. 108 00:10:49,340 --> 00:10:53,360 I'm not going to get you to share two answers in this, but think about what's missing from this. 109 00:10:54,110 --> 00:10:55,280 All I've got is this. I'll. 110 00:10:57,600 --> 00:11:05,940 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.? 111 00:11:06,750 --> 00:11:09,890 Is this okay? No. 112 00:11:10,580 --> 00:11:14,000 You were going. You had lots of things. Okay, here's my list. 113 00:11:14,000 --> 00:11:19,460 And of the lists intersect, intercept, lots missing, lots approximated. 114 00:11:20,390 --> 00:11:26,480 So one which I hinted at is this in fact, is an infectious being compounded. 115 00:11:27,170 --> 00:11:35,030 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. 116 00:11:36,650 --> 00:11:41,000 Maybe you can imagine how we can extend that. We just put another class in between E for exposed. 117 00:11:41,000 --> 00:11:46,460 So you get susceptible, exposed and you're checking away and then you go into infectious. 118 00:11:47,150 --> 00:11:50,980 So we can fix that. There's no host demographics. 119 00:11:50,990 --> 00:11:54,350 This is the only thing that happens to our population. They just stay in recovered forever. 120 00:11:55,670 --> 00:11:59,030 Of course, there should be births and deaths which are nothing to do with the disease. 121 00:11:59,030 --> 00:12:04,309 Right. So newborns, my appearance susceptible and sort of tick through the system. 122 00:12:04,310 --> 00:12:06,860 And there should be natural death from every category. 123 00:12:09,860 --> 00:12:16,580 I've talked about flu and measles, but many of the diseases we care about actually are really complicated with more than one phase. 124 00:12:17,240 --> 00:12:20,120 So HIV, for example, on first infection, 125 00:12:20,450 --> 00:12:27,440 you've got a burst of infectiousness for a few days and then there's a long time period until transition to AIDS. 126 00:12:27,980 --> 00:12:34,790 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. 127 00:12:36,730 --> 00:12:44,830 Spacial dynamics this Peter is is kind of saying every susceptible can contact every infected. 128 00:12:45,670 --> 00:12:49,420 It's like we're in one massive mixing bowl of everyone. Right. 129 00:12:50,080 --> 00:12:59,980 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. 130 00:13:03,190 --> 00:13:06,310 Immunity is not always lifelong and perfect. You can lose immunity. 131 00:13:08,260 --> 00:13:13,000 Life. Oh, I also missed out the possibility you have immunity at birth as maternal immunity. 132 00:13:13,270 --> 00:13:17,770 You have immunity from your mother for the first six months of life, and then that dies down. 133 00:13:17,770 --> 00:13:21,309 And then you have to build up your own life is random. This is a clockwork model. 134 00:13:21,310 --> 00:13:28,420 Essentially. The same thing will happen every time you run it. But stock activity matters, particularly when numbers are slow. 135 00:13:28,430 --> 00:13:32,020 So the time at which this thing takes off should be different. 136 00:13:32,020 --> 00:13:37,720 If I really run it, if I actually had a proper stochastic model, once it gets going, stochastic still less important. 137 00:13:39,560 --> 00:13:45,260 Age structure. So we mentioned spatial structure as a way that people are structured, not all mixing together, 138 00:13:45,770 --> 00:13:51,690 but even if you deal with one town or even one school, it's not that all the kids are mixing equally, right? 139 00:13:51,710 --> 00:13:56,270 There'll be almost a mixing matrix describing how different groups are mixing with each other. 140 00:13:57,890 --> 00:14:02,690 And the special one in blue, which is the one I'm going to talk about virus evolution. 141 00:14:04,410 --> 00:14:08,520 This is about you have one infection, you recover and you stay immune to it forever. 142 00:14:09,660 --> 00:14:15,570 This doesn't work for flu. There's more than one strain for something that strain means. 143 00:14:16,890 --> 00:14:17,190 Okay. 144 00:14:17,190 --> 00:14:24,030 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. 145 00:14:24,990 --> 00:14:30,810 But the fun thing is if you meet someone working on this, which bit of extending okay, 146 00:14:31,560 --> 00:14:37,680 but if you're an expert ready to deal with strains, how do we cope with many strains? 147 00:14:38,040 --> 00:14:42,029 So first, I'm going to show you why this is a really tricky problem and then I'm going 148 00:14:42,030 --> 00:14:45,030 to show you one way we've dealt with this and a little bit of my own work, 149 00:14:46,050 --> 00:14:48,060 but I'm also as well as giving you the results, 150 00:14:48,060 --> 00:14:53,880 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? 151 00:14:53,910 --> 00:14:58,560 Is this just a mathematical exercise? And if I can do that, I'll be really happy. 152 00:14:59,580 --> 00:15:04,830 So quick crash course on influenza for mathematicians. 153 00:15:05,940 --> 00:15:09,929 I'm interested in seasonal influenza. This is not pandemic influenza we're talking about. 154 00:15:09,930 --> 00:15:14,969 Yes, I'm interested in humans. Do you know what many other creatures get? 155 00:15:14,970 --> 00:15:18,800 Flu. I'm interested in humans here. Flu virus. It evolves. 156 00:15:18,810 --> 00:15:23,220 This is a phylogenetic tree of the H3 influenza type. 157 00:15:24,000 --> 00:15:28,410 It evolves to change how it appears. The immune system. Right. 158 00:15:28,440 --> 00:15:33,410 This is a cartoon, but it's these surface proteins actually look like caprese flakes or something. 159 00:15:33,420 --> 00:15:36,750 They're actually they're far more complicated. Here's a bit of them. 160 00:15:37,350 --> 00:15:44,880 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. 161 00:15:45,390 --> 00:15:48,900 So how I'd like you to imagine this is suppose we have one strain, 162 00:15:49,410 --> 00:15:53,850 we have immunity to it either because we've been infected with it and recovered and we've 163 00:15:53,850 --> 00:15:57,960 got a healthy immune system or because we've had the right vaccine for that strain. 164 00:15:59,130 --> 00:16:06,780 But if you change the surface proteins, it's a bit like the influenza is basically disguised itself. 165 00:16:07,530 --> 00:16:15,080 It's not it's not literally like that. But as far as the immune system cares, it's not the same object anymore. 166 00:16:15,090 --> 00:16:18,030 Even though most of it's the same, the bit it first sees is not the same. 167 00:16:19,320 --> 00:16:22,500 And that's a really special property of flu that it can do this continual change. 168 00:16:24,920 --> 00:16:30,320 So this is what we'd like to be able to model. I can't just model is one strain. 169 00:16:31,680 --> 00:16:36,350 But how do we do multiple strains? So you've got this idea, we've got this essay compartmental model. 170 00:16:36,360 --> 00:16:43,799 How do I turn that into a mini strain model? Okay, so let's just go for it's naive approach. 171 00:16:43,800 --> 00:16:50,190 Let's just extend the soil system, okay? Oh, but what does this mean now? 172 00:16:50,340 --> 00:16:57,000 Susceptible to which strain are infected with which strain are recovered from what? 173 00:16:58,410 --> 00:17:01,560 And you think about this really start to realise we need actually lots of different 174 00:17:01,580 --> 00:17:05,940 S's and lots of different eyes and well actually we don't need the owners. 175 00:17:05,940 --> 00:17:12,000 The owners are just a special case of s, so you'd be susceptible to nothing and then you're kind of removed. 176 00:17:13,500 --> 00:17:18,030 So we need more than one s. More than one I. Okay. 177 00:17:19,100 --> 00:17:25,650 You ready to have a go at something? I said, no, let's try and do this between us. 178 00:17:26,790 --> 00:17:32,040 Okay. Let's imagine a disease with two strains and they've been imaginatively named one and two. 179 00:17:33,840 --> 00:17:38,110 What are the classes that we need now? How many of them do we need? What are the classes now? 180 00:17:38,130 --> 00:17:41,820 How many of them do we need? So think about s classes. 181 00:17:42,840 --> 00:17:46,290 How many are we going to need? Maybe don't shout out, but have a think. 182 00:17:47,280 --> 00:17:52,770 So think it through. Okay. So we need someone. We need a class for people who are susceptible to both diseases. 183 00:17:52,780 --> 00:17:55,050 Yeah. So susceptible to one and two. 184 00:17:56,380 --> 00:18:05,050 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. 185 00:18:05,800 --> 00:18:09,010 Yeah. So actually, how many classes have we got now. 186 00:18:10,230 --> 00:18:14,680 Four. And I class is how many of those do we need. 187 00:18:20,390 --> 00:18:35,570 Matt's underground. So you can have a go at this one. Actually more than three. 188 00:18:36,680 --> 00:18:40,250 So you've got people who currently have stream one who previously had nothing. 189 00:18:41,720 --> 00:18:44,480 People who've currently got stream one. If previous you had stream two. 190 00:18:45,830 --> 00:18:50,300 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. 191 00:18:51,260 --> 00:18:55,740 So we chase that through. We've got four. Okay. 192 00:18:56,910 --> 00:19:00,340 That's not too bad for exes and for eyes. Actually, that's absolutely fine. 193 00:19:00,360 --> 00:19:06,120 We're going to look at that further. A much more troubling exercise, if I want to do flu evolution, 194 00:19:06,120 --> 00:19:12,960 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. 195 00:19:13,590 --> 00:19:20,809 How many categories do I need? Lots. 196 00:19:20,810 --> 00:19:23,900 Many, many, many more than I can do on a computer. 197 00:19:25,160 --> 00:19:31,450 Yeah, way more. So it's two to the power of 100, which is about ten to the power of 30. 198 00:19:31,550 --> 00:19:38,900 And it's really bad. It's huge. It's pretty more the number of particles of sand on earth or something and eyeglasses. 199 00:19:39,380 --> 00:19:43,850 Well, it actually goes like end two to the end minus one, which is even worse, actually. 200 00:19:45,530 --> 00:19:52,520 So too many variables is the answer to that. I cannot take this naive approach and do a seasonal flu, which is bad astrology. 201 00:19:54,050 --> 00:20:00,900 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. 202 00:20:00,920 --> 00:20:10,840 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. 203 00:20:11,330 --> 00:20:18,320 The category people have previously had strains one, two, three and four as one for previously and one of for you, this one. 204 00:20:18,350 --> 00:20:22,350 This is sort of a zero with a line through its empty set notation. 205 00:20:22,370 --> 00:20:25,430 So these are people who have previously had no infections. 206 00:20:25,910 --> 00:20:32,000 So this is the category we should be born into in some sense. Then we need some even worse notation for the eyes. 207 00:20:32,000 --> 00:20:37,610 So the superscript is the strain the currently infected with strange six, but they previously had one and three. 208 00:20:38,540 --> 00:20:43,400 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. 209 00:20:44,930 --> 00:20:50,569 So you keep this infection, history and subscripts, but your rates have been infected depends on the subscripts. 210 00:20:50,570 --> 00:20:57,799 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. 211 00:20:57,800 --> 00:21:02,240 You put parameters in to account for cross immunity when you've got it to your accounting rights. 212 00:21:03,440 --> 00:21:08,329 I'm going to show a few slides with quite a lot of equations. 213 00:21:08,330 --> 00:21:11,720 Right. Some of you are going to absolutely love it because you're waiting for some equations. 214 00:21:12,200 --> 00:21:18,290 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. 215 00:21:18,680 --> 00:21:27,560 But I think I need to do this to show you what it is we actually do right outside the two strain model. 216 00:21:28,370 --> 00:21:29,089 One strain model. 217 00:21:29,090 --> 00:21:36,530 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. 218 00:21:37,520 --> 00:21:40,790 So firstly, what do we see? Well, let's start to take it apart. 219 00:21:40,790 --> 00:21:44,270 It's like this. I'll have my variables rate of change down here. 220 00:21:44,300 --> 00:21:47,330 I've got four S's and I've got my four eyes. 221 00:21:47,900 --> 00:21:50,959 And if you think about it, it kind of makes sense as a flow. 222 00:21:50,960 --> 00:21:57,380 So you starts, you've had nothing. We go this way, you have string one but previously had nothing recover. 223 00:21:58,010 --> 00:22:03,740 Now you've had strain one previous you have strain one, got strain two and finally had both. 224 00:22:04,640 --> 00:22:10,520 We can go the other way and get strain two first and then just equations that are connected up in this way. 225 00:22:11,960 --> 00:22:14,690 You probably see a lot of terms are similar between the equations, right? 226 00:22:15,830 --> 00:22:23,090 So these ones with this Greek letter mu if I highlight those, those are all the terms to do with natural births and deaths. 227 00:22:24,020 --> 00:22:27,970 And you can see those one out is up here. So this is got a plus mu everything else is minus. 228 00:22:28,280 --> 00:22:32,000 So the births are going in this everyone born in empty. 229 00:22:34,610 --> 00:22:38,180 So all the other terms. If it's not AMU, it's to do with the infection. 230 00:22:40,250 --> 00:22:45,680 A few other terms. The next most nice ones are these ones with the scanner in front. 231 00:22:46,550 --> 00:22:50,180 Actually, these are all to do with recovery. And this is the flow from eyes back to S's. 232 00:22:50,870 --> 00:22:55,410 Yeah. And that leaves these ones, which is where the action is. 233 00:22:55,440 --> 00:22:58,570 It's flows from essence to wise. 234 00:22:58,590 --> 00:23:03,030 It's infection happening. And maybe you can see a little bit of the asylum model in there. 235 00:23:03,300 --> 00:23:05,330 It still beats at times. Okay. 236 00:23:05,340 --> 00:23:12,720 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. 237 00:23:15,030 --> 00:23:21,750 So this thing I've highlighted in Blue Beta Times, AI is something we call force of infection. 238 00:23:23,020 --> 00:23:26,290 It's the rate a single person will get infected if they're sitting in the system. 239 00:23:26,290 --> 00:23:29,770 It's sort of the pressure to to get infected from the rest of the system. 240 00:23:30,580 --> 00:23:33,850 And actually, we could just well, that's just a mess everywhere. 241 00:23:33,850 --> 00:23:37,480 So let's give it a name. And we always use lambda or the capital lambda or lowercase. 242 00:23:37,630 --> 00:23:41,400 We like concrete letters. So lambda here, lambda one and two. 243 00:23:41,410 --> 00:23:47,060 And if I call that lambda one, call that lambda to, I can immediately make these look much, much less scary. 244 00:23:47,080 --> 00:23:50,910 Yeah. Better or worse? Bit better. 245 00:23:50,920 --> 00:23:59,830 Yeah. Still quite bad. So lambdas are these forces and these flows in between now. 246 00:24:03,030 --> 00:24:09,340 You can see these equations. Well, I still need these eyes in there. 247 00:24:09,350 --> 00:24:12,710 I can't just throw these old equations out because they still appear everywhere. 248 00:24:13,700 --> 00:24:16,910 But there's one very neat move that someone had. 249 00:24:17,270 --> 00:24:23,960 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. 250 00:24:24,860 --> 00:24:28,820 I'm not going to go into the full horror of details of this, but this is the principal idea. 251 00:24:29,360 --> 00:24:37,080 This is the sort of system we've got at the moment. If we short circuit it like this. 252 00:24:38,570 --> 00:24:44,230 It's a much more tractable model. I'm going to be like, hang on, where's the eyeglasses gone? 253 00:24:44,770 --> 00:24:46,870 Well, actually, the following this, they're still in the lambda. 254 00:24:47,530 --> 00:24:53,940 So what happens is now we flow between different classes of s, but it's no longer true compartmental models. 255 00:24:53,950 --> 00:24:58,390 It's not like you're in one of these or one of these. You're exactly in one of these. 256 00:24:58,540 --> 00:25:03,100 But you could also be in one of these. So you can sort of make an overlapping model. 257 00:25:03,520 --> 00:25:09,849 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. 258 00:25:09,850 --> 00:25:15,220 So you're infectious with one. And this turns out to be a really good approximation for short infections. 259 00:25:15,880 --> 00:25:19,480 By short, I mean the infection is a small proportion of your lifetime. 260 00:25:20,290 --> 00:25:24,580 Yeah. So, flu, you're ill for five days. Lifetime, many years. 261 00:25:24,730 --> 00:25:30,459 So that's if you take the ratio of that, it's a small number. So this is really good or a modified model. 262 00:25:30,460 --> 00:25:38,130 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. 263 00:25:38,140 --> 00:25:43,780 You've got to wait there and then go there. Actually, we're quite happy to allow co-infection to happen for flu. 264 00:25:43,780 --> 00:25:49,870 It's possible. So it's already much nicer system now because this is now the full system. 265 00:25:49,870 --> 00:25:53,140 Six equations, eight down to six. 266 00:25:53,170 --> 00:25:56,670 Does that impress you? Okay. 267 00:25:56,700 --> 00:26:01,650 But when I'm dealing with hundredths and order into to the end is now become order to to the end 268 00:26:02,280 --> 00:26:07,440 this this is a good step forward but it's still pretty sucky we can't really do to the end. 269 00:26:08,160 --> 00:26:14,130 So his his our bit of this what we thought that worked well how many of you PhD students. 270 00:26:16,130 --> 00:26:25,250 A few. Right. There's a little window when you know enough about your subjects to understand the background of what's happened. 271 00:26:25,970 --> 00:26:29,660 But you don't know so much. Your mindset is stuck in a particular way. 272 00:26:29,990 --> 00:26:36,080 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. 273 00:26:37,460 --> 00:26:41,720 Enjoy that phase. I was silly enough. 274 00:26:42,520 --> 00:26:48,679 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, 275 00:26:48,680 --> 00:26:54,260 so being an effective susceptibility rather than actually s is the same trick should work nicely. 276 00:26:55,070 --> 00:26:59,030 So I can write these as theatres. Nice looking. 277 00:26:59,030 --> 00:27:05,870 Better and better if I can write some equations for defeated d t with that which don't need the s's. 278 00:27:06,770 --> 00:27:12,649 I'm done. Yeah. I'm going to spare you the details of this. 279 00:27:12,650 --> 00:27:17,480 But if I can do that and what goes in the question marks doesn't depend on any S's. 280 00:27:17,720 --> 00:27:24,060 I've got a closed system here. The bit on short circuiting is my PhD thesis. 281 00:27:24,930 --> 00:27:29,700 Right. I think it's not online and clearly it would take Cambridge servers down if I put it on. 282 00:27:33,060 --> 00:27:37,020 You can get rid of the essays and write things simplified under some assumptions, 283 00:27:37,440 --> 00:27:42,610 some of them a bit technical, but it's related to how partial immunity works and how immunity accumulates. 284 00:27:42,610 --> 00:27:50,610 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. 285 00:27:50,610 --> 00:27:57,450 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. 286 00:27:57,450 --> 00:28:04,740 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. 287 00:28:06,330 --> 00:28:10,049 Impressed yet. Oh, I'm surprised. 288 00:28:10,050 --> 00:28:15,330 You are impressed. We've gone from two to the N, which is a silly number, down to two. 289 00:28:15,330 --> 00:28:21,299 And so 100 strains is 200 variables, which is still quite bad, but I can put it in a computer at that point. 290 00:28:21,300 --> 00:28:27,840 Yeah, it's good news. So that's why it works. 291 00:28:28,980 --> 00:28:34,860 So here's 100 strains with random cross immunity between them computes really large numbers of strains. 292 00:28:34,860 --> 00:28:39,840 I did that on a very old little laptop and no problem you can. 293 00:28:40,650 --> 00:28:45,120 Well, the point of it is you can now add other things. You see all these other complexities. 294 00:28:45,810 --> 00:28:50,100 We've made the strain bit easy. We can do other stuff with it. 295 00:28:53,350 --> 00:29:00,250 There's one figure I have to show you because it's the most expensive plot I have ever made. 296 00:29:00,370 --> 00:29:03,580 I don't have time to tell you that. But the story. 297 00:29:05,400 --> 00:29:09,250 Yeah. Here. 298 00:29:09,250 --> 00:29:13,240 It is horrible, isn't it? It's terrible for many reasons. 299 00:29:13,570 --> 00:29:17,380 So the red colour here means zero. The red colour here means lots. 300 00:29:18,160 --> 00:29:25,180 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. 301 00:29:25,360 --> 00:29:29,500 That's what it's supposed to show, the clusters of strains. It really doesn't need to be in colour. 302 00:29:29,710 --> 00:29:33,280 You agree? Do it in black and white. Perfectly well. I did it in colour. 303 00:29:33,370 --> 00:29:37,209 I submitted it with the paper. And some of you know, that used to be a thing. 304 00:29:37,210 --> 00:29:44,290 And there still is a thing called page charges. And when journals were in print, they charged you a lot, lot more for colour. 305 00:29:44,770 --> 00:29:48,399 And this is the first paper I submitted on my own. Well, I've been in charge of it. 306 00:29:48,400 --> 00:29:56,740 My supervisor was co-author, I had no idea and a massive bill came through for these colour figures that were totally unnecessary. 307 00:29:57,400 --> 00:29:57,820 Bear in mind, 308 00:29:57,820 --> 00:30:02,889 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. 309 00:30:02,890 --> 00:30:09,880 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. 310 00:30:10,570 --> 00:30:16,729 He's like, don't do that can. So we paid for it. 311 00:30:16,730 --> 00:30:21,500 So I'm going to enjoy this thick enough the rest of my career there is okay. 312 00:30:21,530 --> 00:30:25,130 We can model many strains. Julia gets a PhD thesis. 313 00:30:25,520 --> 00:30:29,640 So what's really. What's the point of this? What's where does this go? 314 00:30:29,660 --> 00:30:34,879 Is this just a fun mathematical exercise? It was fun. But the. 315 00:30:34,880 --> 00:30:42,830 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. 316 00:30:45,380 --> 00:30:51,410 But papers don't live this sort of isolated projects in their own right, the scientific threads to all of this. 317 00:30:51,860 --> 00:30:56,419 So we used many results and papers by other researchers and we cite those. 318 00:30:56,420 --> 00:31:05,690 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. 319 00:31:06,950 --> 00:31:11,240 This paper, she says, 250 other papers have used this. 320 00:31:11,900 --> 00:31:16,370 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. 321 00:31:16,820 --> 00:31:20,690 And they've picked these out slightly randomly, not very randomly. 322 00:31:20,690 --> 00:31:24,130 So this is another paper that cited this. 323 00:31:24,140 --> 00:31:30,740 It's also quite a theoretical study, but looking at slightly more general situations as reinfection and vaccination. 324 00:31:33,110 --> 00:31:38,540 There's this paper about Lyme disease. I know nothing about Lyme disease, but turns out it's got strains as well. 325 00:31:38,540 --> 00:31:43,160 So it was useful. The strains are within the tick stage rather than the human stage. 326 00:31:44,480 --> 00:31:48,680 Malaria. And this is genetic Gupta's group here in zoology. 327 00:31:49,460 --> 00:31:53,210 Malaria has strains which are quite different to flu strains. 328 00:31:53,210 --> 00:31:57,410 But some of the mathematics, some of the machinery can be reused between systems. 329 00:32:00,230 --> 00:32:07,060 HPV, human papillomavirus. This is a virus that can cause cervical cancer. 330 00:32:07,070 --> 00:32:11,420 So now it's routinely vaccinated against. But there are multiple types and again, strains. 331 00:32:12,440 --> 00:32:19,860 But this one. This is picked up by a research group in Cologne and used. 332 00:32:20,190 --> 00:32:24,150 Well, you know, I said we didn't do these bigger machine models. Actually, some people do. 333 00:32:24,720 --> 00:32:27,570 So they've got a model that's pulled together a lot of different things. 334 00:32:28,260 --> 00:32:34,320 But the strain bit of it, how you do multiple strains, the epidemiological engine, if you like, is all thing. 335 00:32:35,160 --> 00:32:41,550 So that's a little bit of that study, right? Very, very cool because flu was thing in the end for me. 336 00:32:43,020 --> 00:32:48,540 And a way to understand then how this fits is. Here is a handy small cog I made. 337 00:32:49,630 --> 00:32:53,380 Right. I mean, other people really do have the larger machines. 338 00:32:53,860 --> 00:33:01,659 It gets used in larger machines. And that flu study I showed you, that team actually work for the last couple of years. 339 00:33:01,660 --> 00:33:09,489 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. 340 00:33:09,490 --> 00:33:19,330 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. 341 00:33:19,870 --> 00:33:27,700 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. 342 00:33:28,300 --> 00:33:34,030 So improving it just by Upsilon is worth it, making sure there's a better chance of making a good decision. 343 00:33:35,380 --> 00:33:40,900 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. 344 00:33:41,050 --> 00:33:46,180 It's not us saving the universe, but it fits into other studies which will help improve something. 345 00:33:46,360 --> 00:33:52,509 Yeah. Cool. Pandemic time 2009. 346 00:33:52,510 --> 00:34:01,260 Influenza pandemic. Do you remember this thing? So I'm going to show you some data we've worked on from this. 347 00:34:02,040 --> 00:34:10,620 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. 348 00:34:10,740 --> 00:34:15,750 These are real people. We worked together. Actually, it's all us and UK. 349 00:34:16,300 --> 00:34:20,670 So actually I think there's only one American in that lot. 350 00:34:21,270 --> 00:34:27,750 So it's a very international team. The data we got was based on US medical insurance claims. 351 00:34:28,050 --> 00:34:30,870 So you might have opinions on different health care system systems. 352 00:34:30,870 --> 00:34:35,880 One advantage is if someone goes to their doctor in the US, there has to be a medical insurance claim. 353 00:34:36,090 --> 00:34:41,430 Whether it's going to an insurance company or to Medicare, Medicaid, it has to be coded up. 354 00:34:41,880 --> 00:34:44,880 We have to know what the zip code is, the person who went in. 355 00:34:45,540 --> 00:34:50,010 We know how many of those visits were for influenza like illness. 356 00:34:51,120 --> 00:35:00,590 And the number of total visits where influenza like illness is what it says is the symptoms looked a bit like flu. 357 00:35:00,600 --> 00:35:03,690 There is no swabbing or lab test or sequencing. 358 00:35:03,990 --> 00:35:09,390 There's just someone comes in with symptoms like cough and fever and feeling awful and it kind of looks like flu. 359 00:35:10,890 --> 00:35:17,640 It isn't always flu. You can probably see from that that you have these winter spikes, which are probably flu, 360 00:35:17,640 --> 00:35:21,840 but it never quite goes to zero in the summer, whereas flu literally goes to zero in the summer. 361 00:35:22,200 --> 00:35:28,320 So some of that is allergies, other non-infectious things, plus other viruses. 362 00:35:28,740 --> 00:35:35,910 So you've got this baseline which is probably generally sinusoidal, which is in here sinusoidal and the excess is free. 363 00:35:36,780 --> 00:35:44,400 But a signal in that in 2009, this is what things look like in the US. 364 00:35:45,030 --> 00:35:51,300 So January to April or so you have the normal seasonal flu of the flus that were circulating at time. 365 00:35:51,330 --> 00:35:56,040 At that time here we have a spring wave actually UK. 366 00:35:56,040 --> 00:35:59,490 We had much more of a spring way of things much earlier, much earlier. 367 00:35:59,850 --> 00:36:02,940 And what you'll see is this wasn't all of the US as any bits of the US got this. 368 00:36:02,940 --> 00:36:06,450 And then there was this monster in the autumn and the autumn wave. 369 00:36:06,630 --> 00:36:12,840 The full wave, I should call it. Really. I guess I'm going to show you a movie of this just of the 2009. 370 00:36:14,790 --> 00:36:17,640 These are the different places you recognise. This is the US. 371 00:36:18,090 --> 00:36:24,810 The size of the circle is proportional to the population there, so the area is proportional to population size colour. 372 00:36:25,350 --> 00:36:28,530 I'm getting better with my colour. So green is literally nothing. 373 00:36:28,680 --> 00:36:35,070 And then it goes through to a sort of blue and purple for loads and we're going to start at beginning of 2009. 374 00:36:35,700 --> 00:36:39,000 Remember, this is seasonal. This is spring wave. 375 00:36:39,510 --> 00:36:44,320 That's autumn wave. So seasonal. 376 00:36:50,280 --> 00:36:57,730 Spring wave. And here comes. 377 00:37:05,510 --> 00:37:13,240 The Autumn wave. I really could watch this all day, but I won't. 378 00:37:14,830 --> 00:37:20,240 You see, the seasonal bit does have. Make it once again. 379 00:37:22,250 --> 00:37:28,790 Just once more. It has some patterns. You got a little blip of panic where everyone just has a little panic. 380 00:37:28,790 --> 00:37:32,060 Go to the doctor because Mexican swine flu is here, I guess. 381 00:37:32,270 --> 00:37:35,720 And then you actually have a real spring wave in the northeast in Chicago. 382 00:37:36,260 --> 00:37:43,050 Then the fall wave sort of starts around here. Except for California, which does the same thing. 383 00:37:45,520 --> 00:37:50,320 And it takes weeks and weeks and weeks to get across the US. I mean, you could walk across the US in that time. 384 00:37:51,100 --> 00:37:55,120 It's really slow. So what's going on? 385 00:37:55,930 --> 00:37:59,580 And this is where we need models and maths again. So you've got this datasets. 386 00:38:00,500 --> 00:38:05,290 Higa Can you now tell me, were schools important in spreading this disease? 387 00:38:06,070 --> 00:38:09,130 Now you've got to dissect it using some math. So that's part of our role. 388 00:38:10,030 --> 00:38:19,570 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. 389 00:38:21,370 --> 00:38:28,510 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. 390 00:38:29,320 --> 00:38:34,240 And I've brushed away someone's weeks worth of work to come up with a nice method of doing that. 391 00:38:34,720 --> 00:38:40,990 So there's a bunch of statistics behind this deciding how you do that nicely. You trust we've done that kind of okay. 392 00:38:41,200 --> 00:38:45,999 But you can see there's some ambiguities. You can then colour code places. 393 00:38:46,000 --> 00:38:50,170 So green ones start really early yellow the next wave. 394 00:38:50,170 --> 00:38:54,910 So the colours are now the time of arrival. And you can see it's a beautiful rainbow like thing. 395 00:38:55,480 --> 00:38:59,120 But beautiful in some sense. And they really are different. 396 00:38:59,140 --> 00:39:04,630 So here's the curve for Atlanta City down here and here's for Boston City B in blue. 397 00:39:05,380 --> 00:39:12,100 And they really are separate by ages. It wasn't as if people weren't flying between the two every day. 398 00:39:12,160 --> 00:39:16,090 They were as carefully showing you the east only right. 399 00:39:16,120 --> 00:39:19,900 The rest of the US is complicated and it's not. There's no one there. 400 00:39:19,930 --> 00:39:25,330 There's just not enough that we can really say on sets for sure, for pretty small population sizes. 401 00:39:25,930 --> 00:39:28,630 And you see, California is just its own thing. 402 00:39:31,350 --> 00:39:37,319 So you can do statistics like say correlate onset time with school opening because this is happening over August, 403 00:39:37,320 --> 00:39:42,660 September or October and schools in the US go back at different times depending on which state you're in. 404 00:39:42,930 --> 00:39:46,020 So the southern states go back earlier and the northern states go back later. 405 00:39:46,590 --> 00:39:50,700 And you know what? The onset correlates beautifully with school opening. 406 00:39:51,990 --> 00:39:55,500 But before you're too quick to blame the schools, there's the diagonal, as it were. 407 00:39:56,280 --> 00:40:00,570 And you can see, yes, it correlates, but it's not quite explained by schools open. 408 00:40:00,900 --> 00:40:07,320 And then influenza hits a week later. Schools open and influenza hits a month later. 409 00:40:07,440 --> 00:40:15,390 So it's not quite the whole story. In fact, you can get as good a correlation just by looking at great circle distance. 410 00:40:15,820 --> 00:40:19,650 I haven't said where from. But zero is a place called both in Alabama. 411 00:40:22,490 --> 00:40:27,120 It's the first place that popped up. I used to ask and talk to anyone ever been there? 412 00:40:27,140 --> 00:40:30,710 And then someone said Yes, one day I'm going to do that again. 413 00:40:32,600 --> 00:40:35,870 There was a lot of talk at the time. Is climate and weather being important? 414 00:40:36,140 --> 00:40:43,190 Do you know what this thing correlates with? Humidity as well. As you increase absolute humidity, the onset date becomes earlier. 415 00:40:43,670 --> 00:40:49,370 I'll separate at eight Eastern movies. But all of these all of these correlations I've shown you are ridiculously significant. 416 00:40:50,540 --> 00:40:53,750 So you get this phase of panic of the pandemic. Oh, yes. It's all about schools. 417 00:40:54,200 --> 00:41:00,439 It's all about humidity. It's pure geographic. And then you start to suspect your colleagues have lost the plot. 418 00:41:00,440 --> 00:41:04,070 Really? And you have to show them a really silly correlation to get in, to get over it. 419 00:41:04,520 --> 00:41:09,070 So silly correlation here. You want something that correlates with this. 420 00:41:09,140 --> 00:41:12,170 It's different in the south and the northeast, right? 421 00:41:13,100 --> 00:41:21,050 So you come up with some suitable quantity and you correlate it. 422 00:41:21,720 --> 00:41:25,340 It's just this is Obama is the nearest time. And you know what? 423 00:41:25,370 --> 00:41:33,500 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. 424 00:41:34,020 --> 00:41:38,210 No, it didn't. It's just everything correlates. There's a spatial pattern, right? 425 00:41:38,810 --> 00:41:45,650 Any spatial pattern in correlated with anything you like. And you can have fun submitting papers under the names of your enemies for these. 426 00:41:47,480 --> 00:41:52,190 So which factors actually matter? Right. If you want want to take this apart, you can't just do it by correlations. 427 00:41:53,180 --> 00:41:58,129 You really need to construct a spatial model. And this is sort of stuff you do. 428 00:41:58,130 --> 00:42:01,610 Then build a model and disentangle it and try and see what matters. 429 00:42:01,940 --> 00:42:07,730 So going to make model where we include humidity, don't include humidity, see if it's okay with or without, see what matters. 430 00:42:08,570 --> 00:42:16,340 And the force infection between cities. It's force of infection against the same thing, sort of a rate or pressure of getting infected. 431 00:42:16,850 --> 00:42:19,880 But rather than thinking about individual people now, think about cities. 432 00:42:20,390 --> 00:42:24,950 Yeah. So red city here is infected pandemics well and truly taken off there. 433 00:42:25,250 --> 00:42:34,700 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. 434 00:42:36,350 --> 00:42:44,929 Then you put in every factor that everyone suggested is importance, not voting patterns we didn't put in might depend on population size, 435 00:42:44,930 --> 00:42:49,100 and each place might depend on where the schools have started in the target place, 436 00:42:49,580 --> 00:42:52,910 humidity in the target place, and of course, the distance between them, 437 00:42:53,150 --> 00:42:56,780 whether people can actually travel between them easily or whether they're just opposite ends of the country. 438 00:42:57,830 --> 00:43:06,650 You throw it all in and give me the schematic idea here, which is we've got a probabilistic model now. 439 00:43:07,100 --> 00:43:11,450 It's it's no longer deterministic. It's probably stochastic. 440 00:43:11,450 --> 00:43:15,140 So I think we need to run it a lot of times. So we need to do some clever stuff with likelihoods. 441 00:43:16,310 --> 00:43:19,580 We've got these observations here. Here's what actually happened in 2009. 442 00:43:19,580 --> 00:43:23,780 Once, what's the chances of observing this thing given this model? 443 00:43:24,650 --> 00:43:27,440 So for each one of our models and we've got a lot of models, 444 00:43:27,890 --> 00:43:35,660 you then change your parameters here to make this as likely as possible to fit its maximum likelihood style to this thing. 445 00:43:37,040 --> 00:43:44,510 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, 446 00:43:44,520 --> 00:43:50,810 but I think this is conceptually the worst slide because each of these rows represents a class of models. 447 00:43:50,840 --> 00:43:54,200 Actually, within each one there's many dozens of models. I'm going to pick the best one. 448 00:43:55,430 --> 00:43:59,480 Do they include local transmission? Do they include schools been on or off? 449 00:44:00,350 --> 00:44:01,610 Do they include humidity? 450 00:44:02,210 --> 00:44:08,690 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? 451 00:44:08,690 --> 00:44:15,139 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. 452 00:44:15,140 --> 00:44:18,650 Okay. And good, which is pretty much what it does anyway. 453 00:44:19,700 --> 00:44:25,130 And these are the eight possibilities of mixing these three on and off. 454 00:44:25,490 --> 00:44:29,360 You can see the first four. If you don't include local transmission, the fit is terrible. 455 00:44:29,360 --> 00:44:32,689 It will always be terrible. That should have been obvious to you from the movie. 456 00:44:32,690 --> 00:44:39,049 The you could see is like a wave, right? So the ones that do include it are basically all at least. 457 00:44:39,050 --> 00:44:42,740 Okay, all good. Can you see what factor is next? 458 00:44:42,740 --> 00:44:47,460 Most important there. Yeah. 459 00:44:48,030 --> 00:44:51,290 So the two with schools not been considered okay. 460 00:44:51,300 --> 00:44:56,370 The two with them are pretty good. So it's better to include them and humidity. 461 00:44:59,010 --> 00:45:03,960 It doesn't really do anything by the time you've accounted for everything else. Humidity doesn't add anything. 462 00:45:04,620 --> 00:45:07,560 So in parsimony we say, okay, it's a non-issue. 463 00:45:07,770 --> 00:45:15,299 Humidity was not important, at least for the onset of pandemic, and 2009 may have been important for how severe infections were. 464 00:45:15,300 --> 00:45:19,320 But in terms of arrival, some of you would like to actually see the model, right? 465 00:45:21,230 --> 00:45:24,540 Okay. It's a lambda is a force of infection. 466 00:45:25,170 --> 00:45:28,620 We just throw lots of stuff in this humidity. There's weather. There was a spring wave. 467 00:45:28,620 --> 00:45:37,260 External seating indicator functions for schools in each place, population sizes, a distance function and this fun normalisation thing. 468 00:45:37,860 --> 00:45:39,930 And then you can build up a likelihood model from there. 469 00:45:40,740 --> 00:45:45,960 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. 470 00:45:47,250 --> 00:45:51,990 We found, of course, it was strong short range transmission. Nearby cities infected each other. 471 00:45:52,680 --> 00:45:55,720 You got occasional long range or even international transmission. 472 00:45:55,740 --> 00:46:02,550 California was a jump. It had just clearly come over internationally or the whole way across the country at the time. 473 00:46:03,000 --> 00:46:07,950 Schools, yeah, slightly important, but not very humidity. 474 00:46:07,980 --> 00:46:15,030 No, population size is slightly, but that's a tricky one because the cities are sort of normalised in some sense already. 475 00:46:16,020 --> 00:46:19,469 But let's have a little think about this. 476 00:46:19,470 --> 00:46:24,510 One city infecting another actually means and why you should be a little troubled by this. 477 00:46:25,560 --> 00:46:32,400 So again, the models we build aren't necessarily all the models in the world, it's the ones that we think of. 478 00:46:32,400 --> 00:46:35,430 And that's very much shaped by our understanding of how things work. 479 00:46:35,880 --> 00:46:40,800 So trial models shaped by current knowledge us is tricky. 480 00:46:40,800 --> 00:46:46,620 So let's do something closer to home, right? And choose two cities at random. 481 00:46:47,820 --> 00:46:52,590 Let's call them out and see. This is my commute each week. 482 00:46:53,940 --> 00:47:03,210 If only there was a road which went like the arrow. So I'm talking about Oxford infecting Cambridge. 483 00:47:05,640 --> 00:47:10,440 What crazy world is this? This is like some giant sneeze from Oxford to Cambridge. 484 00:47:10,770 --> 00:47:17,310 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. 485 00:47:19,140 --> 00:47:26,219 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. 486 00:47:26,220 --> 00:47:29,070 But underlying it, of course, is a much more detailed model. 487 00:47:29,490 --> 00:47:37,649 So maybe let's suppose a pandemic is hit, some people are infected and not everyone and no one say infection. 488 00:47:37,650 --> 00:47:41,580 How does it get between the cities without massive sneeze? See me can't sneeze at four. 489 00:47:42,480 --> 00:47:47,440 I could think of three ways. Yeah. Maybe you've thought of one. 490 00:47:47,440 --> 00:47:50,350 Maybe you just thought of the second. I wonder which ones. 491 00:47:51,430 --> 00:48:02,770 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. 492 00:48:02,980 --> 00:48:06,220 Right. So an infected can travel to the other city. 493 00:48:06,250 --> 00:48:10,330 That's one way of doing it. Not the only way. Can you. Can you now think of another way? 494 00:48:10,370 --> 00:48:15,140 So it's this reset that. Yeah, exactly. 495 00:48:15,170 --> 00:48:25,190 Other way. So someone who's susceptible in Cambridge like me comes and hangs out in Oxford for a while and captures of someone, 496 00:48:25,190 --> 00:48:29,450 takes it back and goes and affects all of Cambridge. That's another way. 497 00:48:30,260 --> 00:48:35,390 Can you think of a third way of doing this? Yes, I saw some of that. 498 00:48:35,780 --> 00:48:41,569 Yeah, of course. You can have someone. There's a third party city that people go to. 499 00:48:41,570 --> 00:48:45,530 Infection happens and yeah. Go home, infect everyone. 500 00:48:46,700 --> 00:48:52,680 So I've somehow fudged. And this is this is a more realistic model, still bonkers. 501 00:48:53,330 --> 00:48:59,420 But to get this right, I'd need to know how everyone in Oxford and Cambridge moves where they go, 502 00:48:59,420 --> 00:49:03,470 where they hang out, where they spend their time and build a massive model out of that. 503 00:49:03,680 --> 00:49:07,310 And you can see we're very quickly into London, complete bonkers, right? Cause we can't do this. 504 00:49:09,200 --> 00:49:13,870 What we do instead is think of it in a far simpler way. 505 00:49:13,880 --> 00:49:21,470 And just so there's a probability of people infection getting from here to here by one of those three means, 506 00:49:21,470 --> 00:49:27,860 and it depends on the distance between the towns. So it tells of exponential models what we typically use because it fits jolly well. 507 00:49:29,720 --> 00:49:37,190 You could see, you know, we don't literally believe this is true, but it's simple to work with. 508 00:49:37,190 --> 00:49:41,059 It's good enough. You can also check how robust things are because we can change this a bit. 509 00:49:41,060 --> 00:49:45,600 We can pull it in a bit tighter, a bit looser, and see if our main results don't change. 510 00:49:46,550 --> 00:49:52,430 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. 511 00:49:52,850 --> 00:50:01,670 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, 512 00:50:02,990 --> 00:50:07,190 screwing around with the picture of Hannah Fry on my tummy. Go the BBC pandemic. 513 00:50:08,360 --> 00:50:12,830 This is not real pandemic, but. But it's a virtual pandemic. 514 00:50:14,270 --> 00:50:17,540 We have a mobile phone app. Has anyone done this? 515 00:50:19,610 --> 00:50:26,269 Oh, new people. All right, so we actually members BBC pandemic. 516 00:50:26,270 --> 00:50:34,100 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. 517 00:50:35,060 --> 00:50:42,780 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. 518 00:50:42,800 --> 00:50:51,200 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. 519 00:50:51,800 --> 00:50:57,320 But it's also a really big citizen science project. Real data is being collected. 520 00:50:57,320 --> 00:51:04,580 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, 521 00:51:04,580 --> 00:51:13,340 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. 522 00:51:13,580 --> 00:51:15,950 Right. This is the one you can take part in. It's still running now. 523 00:51:17,240 --> 00:51:22,310 So the collection is once you agree to do this, you need to be 13 or over to do this. 524 00:51:22,820 --> 00:51:26,120 Otherwise, I'm afraid we have to throw away your data collection. 525 00:51:26,120 --> 00:51:33,649 Period is 24 hours and when you press go it record once per hour where you are down to square kilometre. 526 00:51:33,650 --> 00:51:38,059 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. 527 00:51:38,060 --> 00:51:42,410 And some square kilometre mesh is a short survey at the start where you say, 528 00:51:42,410 --> 00:51:46,520 Answer a few questions about yourself and there's a contact survey at the end, 529 00:51:46,820 --> 00:51:50,389 which is how many people did you actually interact with over the last 24 hours? 530 00:51:50,390 --> 00:51:53,570 Tell us a little bit about them. Was the context work or school or home? 531 00:51:54,730 --> 00:51:59,000 And you can do more than one day if you like, but doing at least one day would be really useful to us. 532 00:51:59,480 --> 00:52:05,930 So if you're happy with this and one kilometre every hour is not particularly intrusive, please go and do it. 533 00:52:06,200 --> 00:52:10,340 We need as many people as possible and a diverse group as possible to do this. 534 00:52:10,610 --> 00:52:13,880 Don't even worry about which day you're doing. Just choose any random day. 535 00:52:14,040 --> 00:52:19,310 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. 536 00:52:21,390 --> 00:52:25,280 That's a national. But what about Heysel myth? Why does the country need Heysel? 537 00:52:25,280 --> 00:52:29,390 May Well, this has already happened, actually, I have to confess. 538 00:52:29,930 --> 00:52:33,890 So this was much more intrusive. It was collection period of three days. 539 00:52:35,390 --> 00:52:40,190 The recordings were as frequent as a mobile phone would do without emptying its batteries completely. 540 00:52:40,190 --> 00:52:47,900 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. 541 00:52:49,250 --> 00:52:53,840 And here's a little zoom in of Haslemere. We have a uniquely detailed study of one towns. 542 00:52:53,840 --> 00:52:58,280 We know what an epidemic in this community would look like in great detail because we know how people move. 543 00:52:59,120 --> 00:53:02,660 We've done it. I can't tell you what happened. 544 00:53:02,810 --> 00:53:09,650 You got to watch the programme, but it worked. I'll tell you that much just to show you there are mathematicians behind. 545 00:53:09,650 --> 00:53:13,070 This is also we've got a team of four of us who are during the number. 546 00:53:13,320 --> 00:53:17,250 Working behind the scenes for Petra. Stephen Maria a must see. 547 00:53:17,250 --> 00:53:24,660 I got my thinking face again. This is us actually in hazmat ready for the filming for the big reveal at the end. 548 00:53:25,260 --> 00:53:28,290 And this is what our Sunday a few weeks looked like. 549 00:53:28,560 --> 00:53:32,130 1 a.m. The collection was Thursday, Friday, Saturday. 550 00:53:32,260 --> 00:53:40,560 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. 551 00:53:41,280 --> 00:53:43,870 We finished running the simulations of the hazelnut epidemic. 552 00:53:43,870 --> 00:53:47,430 There's some work to be done tidying up with data and then running it and then verifying it. 553 00:53:47,730 --> 00:53:51,990 And the longer we work into the night, the more we have to recheck things. We don't trust what we're doing anymore. 554 00:53:52,470 --> 00:53:58,410 We actually finished for him, which is earlier than we'd hoped. 10 a.m. we went to Hazmat 2 p.m. 555 00:53:59,010 --> 00:54:01,650 I don't quite notice I was going to be stuck on camera that day. 556 00:54:02,310 --> 00:54:07,830 So if you watch the programme and I'm like, I have bad luck on that day, you forgive me, that's what happened. 557 00:54:09,090 --> 00:54:10,680 That's those in Hazmat beforehand. 558 00:54:10,680 --> 00:54:17,280 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. 559 00:54:17,760 --> 00:54:26,610 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. 560 00:54:27,300 --> 00:54:32,760 But why mislead to both the Hazel Wear study, which is really detailed and quite big, 561 00:54:32,760 --> 00:54:36,150 and the national study which is already monster big and I hope more people do it. 562 00:54:36,840 --> 00:54:43,230 So we might be able to answer things like how far do people actually move on a typical day on average, 563 00:54:43,240 --> 00:54:48,060 I'm not talking about air travel, I'm talking about normal day to day movement. How does it vary by age group. 564 00:54:48,660 --> 00:54:52,260 We could probably all sit down and try and imagine how that is, but do we know for sure? 565 00:54:52,260 --> 00:54:55,650 And from what we've seen already, our assumptions don't work. 566 00:54:56,730 --> 00:55:03,540 Here's here's a fun one. Do people in larger cities move more or less than people are in more rural areas? 567 00:55:05,310 --> 00:55:10,379 You sort of think of cities as movement and rural. You stay in that same place while fishing of the US. 568 00:55:10,380 --> 00:55:15,510 Data suggests that the reverse is true, but we can't actually find any data to verify that. 569 00:55:15,510 --> 00:55:16,469 But we should be able to. 570 00:55:16,470 --> 00:55:23,730 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. 571 00:55:24,840 --> 00:55:29,700 There's a week. How a Saturday is different Wednesdays do people move? 572 00:55:29,700 --> 00:55:36,810 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. 573 00:55:37,980 --> 00:55:41,670 So there it is. So hopefully we can answer some of that with the BBC pandemic data. 574 00:55:42,180 --> 00:55:49,020 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. 575 00:55:49,020 --> 00:55:50,520 We're going to pick it up and hype it. 576 00:55:50,940 --> 00:55:57,660 But of course, what we're producing and this will go to the scientific community in the end is another small cog, 577 00:55:59,310 --> 00:56:06,480 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. 578 00:56:06,480 --> 00:56:12,960 In the UK there'll be some research papers and I'm into flu, but they won't all be flu. 579 00:56:12,990 --> 00:56:16,860 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. 580 00:56:17,460 --> 00:56:26,160 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. 581 00:56:26,910 --> 00:56:32,160 We don't know what, but we feed into the scientific threat and hope it will be picked up by others. 582 00:56:32,160 --> 00:56:36,000 Our job is to communicate what we know about this data and to share it with others. 583 00:56:37,650 --> 00:56:43,110 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. 584 00:56:43,110 --> 00:56:49,920 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. 585 00:56:50,940 --> 00:56:53,040 Thank you all very much for coming tonight and thanks for listening.