WEBVTT 00:00:15.683 --> 00:00:19.379 One hundred years ago, a new influenza virus emerged, 00:00:19.379 --> 00:00:23.248 spread around the world and killed 50 to 100 million people. 00:00:23.748 --> 00:00:26.989 For every 40 people that got this influenza infection, 00:00:26.989 --> 00:00:28.586 one of them died. 00:00:28.586 --> 00:00:31.331 And you think, maybe that's not that bad odds, 00:00:31.331 --> 00:00:33.770 but for the most recent influenza pandemic, 00:00:33.770 --> 00:00:37.559 for each person that died there were probably 10,000 cases. 00:00:37.949 --> 00:00:40.936 Which means that this 1918 influenza pandemic 00:00:40.936 --> 00:00:43.256 was the worst pandemic in history. 00:00:43.459 --> 00:00:47.015 Here's a graph showing the weekly deaths at the time of the pandemic 00:00:47.015 --> 00:00:49.486 in New York, London, Paris and Berlin. 00:00:49.866 --> 00:00:54.337 You can quite clearly see in the middle, the major wave of the pandemic. 00:00:54.467 --> 00:00:57.152 And so all the way from North America to Europe, 00:00:57.152 --> 00:00:59.966 this pandemic was happening at the same time. 00:00:59.966 --> 00:01:04.543 And this synchronicity, this is a common feature of influenza pandemics. 00:01:05.273 --> 00:01:08.995 So not only was there this major influenza pandemic in 1918, 00:01:08.995 --> 00:01:11.989 but it was also the tail end of the First World War. 00:01:12.249 --> 00:01:14.272 And I've marked here the Armistice, 00:01:14.272 --> 00:01:17.331 so the official end of the First World War, in white. 00:01:17.621 --> 00:01:22.450 So you can see here that not only was this a terrible time for Europe, 00:01:22.450 --> 00:01:25.353 but data were being collected on deaths. 00:01:25.353 --> 00:01:28.877 And this really showed that infectious diseases are a priority 00:01:28.877 --> 00:01:31.093 and that we need to collect these kind of data 00:01:31.093 --> 00:01:34.699 to understand how and why these epidemics happen. 00:01:35.211 --> 00:01:39.626 So computational and mathematical tools can be used on data like these 00:01:39.626 --> 00:01:43.744 to understand the transmission processes and how the epidemic is occurring 00:01:43.744 --> 00:01:49.223 with the ultimate aim of trying to develop interventions, so control methods, 00:01:49.223 --> 00:01:53.244 to curtail the epidemic and to slow down transmission. 00:01:53.894 --> 00:01:57.926 So, the difference between epidemics and pandemics is one of scale. 00:01:57.926 --> 00:02:00.738 Since they're Greek words, you probably already know them, 00:02:00.738 --> 00:02:03.831 but for those who aren't, I'll just briefly explain. 00:02:03.931 --> 00:02:07.360 An epidemic is geographically localized to one place. 00:02:07.360 --> 00:02:13.334 So for instance, the recent Ebola epidemic in West Africa was confined to West Africa 00:02:13.334 --> 00:02:15.346 and is therefore an epidemic. 00:02:15.346 --> 00:02:18.912 The 1918 influenza pandemic, that spread around the world. 00:02:18.912 --> 00:02:21.878 And spreading around the world is what defines a pandemic. 00:02:21.878 --> 00:02:25.228 When we get any new epidemic, one thing that we're really interested in 00:02:25.228 --> 00:02:27.979 is how quickly it's spreading from person to person. 00:02:27.979 --> 00:02:31.244 And we define this as the reproduction number. 00:02:31.244 --> 00:02:35.047 So the reproduction number is the average number of new cases 00:02:35.047 --> 00:02:38.308 that each infectious person causes at the start. 00:02:38.308 --> 00:02:39.797 So if you were the first person 00:02:39.797 --> 00:02:43.124 that got an epidemic, or got a new virus or a new pathogen, 00:02:43.124 --> 00:02:46.676 and nobody else had had it, how many people would you infect? 00:02:46.676 --> 00:02:50.968 So let's take, for example, that one infectious person walks into the room. 00:02:51.068 --> 00:02:56.404 And if the reproduction number is two, we expect two new cases from that person. 00:02:56.674 --> 00:03:00.577 And if those two people go off and infect two more of their friends, 00:03:00.577 --> 00:03:03.532 well, they might not have two friends anymore, 00:03:03.532 --> 00:03:05.844 but we now have four cases. 00:03:05.844 --> 00:03:10.656 And then if those four infect two more each and so on and so forth, 00:03:10.656 --> 00:03:13.063 you can see that the epidemic will grow. 00:03:13.453 --> 00:03:15.054 So the reproduction number, 00:03:15.054 --> 00:03:18.658 the average number of people that each infectious person infects, 00:03:18.658 --> 00:03:22.603 really determines how quickly the epidemic grows. 00:03:22.603 --> 00:03:25.733 OK, well, this is true, especially in the beginning. 00:03:25.733 --> 00:03:30.118 But, if you carried on like this with each person infecting two, 00:03:30.118 --> 00:03:32.913 step by step, as we've shown here, 00:03:32.913 --> 00:03:37.637 by the 33rd step, you would have infected everybody on earth. 00:03:37.637 --> 00:03:39.549 And we know that that doesn't happen. 00:03:39.549 --> 00:03:43.312 So, why is it that that doesn't happen? 00:03:43.492 --> 00:03:46.733 Well, this is because you start to run out of susceptible people, 00:03:46.733 --> 00:03:48.772 so people who haven't had the infection, 00:03:48.772 --> 00:03:51.775 and this is called depletion of susceptibles. 00:03:51.775 --> 00:03:55.311 So, to demonstrate this, let's imagine that this person here, 00:03:55.311 --> 00:03:57.057 we'll call her Christina, 00:03:57.057 --> 00:03:59.493 Christina was infected in the second step, 00:03:59.493 --> 00:04:01.586 which seems like pretty bad luck. 00:04:01.586 --> 00:04:04.271 Christina happens to be friends with Spyros. 00:04:04.771 --> 00:04:10.063 So when Spyros gets infected later, and he tries to infect two more, 00:04:10.063 --> 00:04:12.910 one of the people he tries to infect is Christina. 00:04:13.510 --> 00:04:15.182 But she's already had it. 00:04:15.182 --> 00:04:20.203 So here she is colored in blue because she's has got immunity to infection 00:04:20.203 --> 00:04:21.890 now that she's recovered. 00:04:21.890 --> 00:04:24.452 So when Spyros tries to infect her, he can't, 00:04:24.452 --> 00:04:28.184 and that means that the number infected slows down. 00:04:28.184 --> 00:04:32.135 And if this is true for other people in the population, like this, 00:04:32.135 --> 00:04:35.981 then you start to see a slow down in the number of people infected. 00:04:35.981 --> 00:04:38.084 So this is depletion of susceptibles. 00:04:38.084 --> 00:04:41.794 And I'll show you how we incorporate these kind of processes 00:04:41.794 --> 00:04:43.662 into models of transmission. 00:04:44.782 --> 00:04:46.932 If we were going to model something like flu, 00:04:46.932 --> 00:04:49.412 the first thing we would do is divide the population 00:04:49.412 --> 00:04:51.428 into three disease groups. 00:04:51.578 --> 00:04:54.814 So here you can see people who are susceptible to infection, 00:04:54.814 --> 00:04:56.633 so they're able to get infected. 00:04:56.713 --> 00:05:00.235 You can see infectious people who have got the infection 00:05:00.235 --> 00:05:02.248 and are spreading it to other people. 00:05:02.248 --> 00:05:06.133 And then you've got in blue the recovered or died group. 00:05:06.133 --> 00:05:09.048 So normally we assume that when people recover from infection, 00:05:09.048 --> 00:05:10.211 they are protected. 00:05:10.211 --> 00:05:14.176 But if it's a very severe infection, they may also have died. 00:05:14.176 --> 00:05:17.396 And everybody in the population has to be one of these groups. 00:05:17.396 --> 00:05:23.400 And we determine the rates of transition between each group. 00:05:23.400 --> 00:05:27.147 So when you get infected, this happens at the rate of transmission, 00:05:27.147 --> 00:05:30.966 and then when people recover, this happens at the rate of recovery. 00:05:30.966 --> 00:05:33.910 So this rate of transmission is the most important one 00:05:33.910 --> 00:05:36.988 when we're thinking about how quickly epidemics grow. 00:05:36.988 --> 00:05:41.784 What we want to define is when you have an infectious person in the population 00:05:41.784 --> 00:05:45.825 and they go out and they make contacts with the people that they know, 00:05:45.825 --> 00:05:50.480 how likely are they to pass that infection on to their contacts? 00:05:50.800 --> 00:05:54.642 And so, what we do when we mathematically define the rate of transmission 00:05:54.642 --> 00:05:57.053 is we're going to divide it into four parts. 00:05:57.053 --> 00:05:59.923 So first of all, we have our rate of transmission 00:05:59.923 --> 00:06:03.425 is equal to the number of infectious people. 00:06:03.425 --> 00:06:05.339 So the more infectious people there are, 00:06:05.339 --> 00:06:07.354 the higher the rate of transmission will be 00:06:07.354 --> 00:06:11.030 because there's a lot of people around infecting people. 00:06:11.630 --> 00:06:16.302 Then we multiply it by the number of contacts that each person has on average. 00:06:16.302 --> 00:06:21.025 So you can see here that the infectious people make those contacts at random 00:06:21.025 --> 00:06:25.008 with susceptible, infectious or recovered people. 00:06:25.258 --> 00:06:28.854 Then we include the probability of infection on a contact. 00:06:28.854 --> 00:06:30.044 So what is the chance 00:06:30.044 --> 00:06:32.782 that when an infectious person meets a susceptible person 00:06:32.782 --> 00:06:34.742 they give them the infection? 00:06:34.742 --> 00:06:38.637 For flu, this is probably around 10%, something like that. 00:06:39.137 --> 00:06:41.997 And then finally, we include the proportion of the population 00:06:41.997 --> 00:06:43.574 who are susceptible. 00:06:43.574 --> 00:06:47.654 So at the beginning of an epidemic, when most people are susceptible, 00:06:47.654 --> 00:06:49.364 so they haven't had it, 00:06:49.364 --> 00:06:53.763 the probability that you meet a susceptible person is quite high. 00:06:53.763 --> 00:06:58.949 But later, as this pool is depleted, so you run out of susceptible people, 00:06:58.949 --> 00:07:02.824 it becomes less likely that you'll meet a susceptible individual. 00:07:02.934 --> 00:07:07.482 So let's see how this is incorporated into our models. 00:07:07.952 --> 00:07:10.194 So this is what an epidemic looks like - 00:07:10.194 --> 00:07:13.174 a simulated epidemic in 5,000 people. 00:07:13.284 --> 00:07:16.707 You can see the grey bar marks the susceptible group, 00:07:16.707 --> 00:07:19.174 and it starts at 5,000, which is everybody, 00:07:19.174 --> 00:07:21.978 apart from one infectious person at the beginning. 00:07:22.250 --> 00:07:24.891 In red you can the infectious epidemic, 00:07:24.891 --> 00:07:28.141 and then in blue, the recovered group at the end. 00:07:28.561 --> 00:07:31.427 So what you might notice is that at this point, 00:07:31.427 --> 00:07:35.179 when half of the susceptible individuals have been infected, 00:07:35.179 --> 00:07:38.742 this part of the equation, the proportion of the susceptible, 00:07:38.742 --> 00:07:40.321 is also halved, 00:07:40.451 --> 00:07:43.745 which really pushes down the rate of transmission. 00:07:43.745 --> 00:07:46.902 And that's important, because it's this depletion of susceptibles, 00:07:46.902 --> 00:07:48.948 so running out of susceptible people, 00:07:48.948 --> 00:07:52.578 that causes the epidemic to peak and then decline. 00:07:53.108 --> 00:07:57.089 Now, the eagle-eyed among you might have also noticed 00:07:57.089 --> 00:08:02.331 that if you draw a horizontal line at 5,000, which is the total population, 00:08:02.331 --> 00:08:05.815 that by the end of the epidemic there's a small gap. 00:08:05.965 --> 00:08:09.134 There's a gap between the total number of susceptible people 00:08:09.134 --> 00:08:12.372 and the number of people that were infected in total. 00:08:12.482 --> 00:08:16.032 And that's because some people don't get infected. 00:08:16.032 --> 00:08:17.584 The lucky ones. 00:08:17.584 --> 00:08:22.584 So this total number of people infected and the size of the gap 00:08:22.584 --> 00:08:27.459 is determined by the reproduction number, by how infectious the pathogen is. 00:08:27.949 --> 00:08:31.476 So let's explore how that relationship looks. 00:08:31.476 --> 00:08:33.435 So what I'm showing you here, 00:08:33.435 --> 00:08:39.075 on the horizontal axis you can see reproduction numbers from zero to five. 00:08:39.075 --> 00:08:42.278 And on the vertical axis you can see the percent of the population 00:08:42.278 --> 00:08:44.672 that are infected in total. 00:08:44.672 --> 00:08:47.815 So let's take a look at some pathogens that you might have heard of 00:08:47.815 --> 00:08:50.380 and see what their reproduction numbers are. 00:08:50.767 --> 00:08:56.640 So here, for example, seasonal influenza, probably around 1.4-1.5. 00:08:57.110 --> 00:09:00.540 Ebola, that's around 2. 00:09:01.085 --> 00:09:03.927 Pandemic flu, maybe 2.5. 00:09:03.927 --> 00:09:06.748 SARS, around 3. 00:09:06.748 --> 00:09:09.238 And then smallpox, around 5. 00:09:09.238 --> 00:09:14.646 So for every case of smallpox that we could see in the population, 00:09:14.646 --> 00:09:18.235 we would expect to see five more smallpox cases. 00:09:18.235 --> 00:09:20.787 So, what's the relationship? 00:09:20.787 --> 00:09:24.635 Here you can see that from zero to one, 00:09:24.635 --> 00:09:27.075 when the reproduction number is less than one, 00:09:27.075 --> 00:09:28.844 nobody is infected. 00:09:28.844 --> 00:09:31.603 And that's because if you infect less than one person 00:09:31.603 --> 00:09:34.835 for each infectious person, there's no epidemic. 00:09:34.835 --> 00:09:36.651 And then it takes off rapidly, 00:09:36.651 --> 00:09:39.688 and it appears to approach 100%. 00:09:39.688 --> 00:09:41.255 But it doesn't quite. 00:09:41.255 --> 00:09:44.045 That line doesn't quite reach 100%. 00:09:44.045 --> 00:09:48.391 And to show you that, let's take a look at even higher reproduction numbers. 00:09:48.771 --> 00:09:50.851 So here you can see the same graph, 00:09:50.851 --> 00:09:54.911 but now the horizontal axis starts at five and runs till 10, 00:09:54.911 --> 00:09:57.938 and the vertical axis is much higher. 00:09:57.938 --> 00:10:03.249 So some pathogens in this region are pertussis, which causes whooping cough, 00:10:03.249 --> 00:10:06.573 and polio and diphtheria are also around here. 00:10:06.573 --> 00:10:12.145 So again you see the line increases as the reproduction number gets higher. 00:10:12.145 --> 00:10:16.772 But it still doesn't reach 100% even though it looks like it. 00:10:16.892 --> 00:10:21.541 OK, so what about if it's even, even higher than that? 00:10:21.791 --> 00:10:23.926 So let's take a look now, the same graph, 00:10:23.926 --> 00:10:28.897 but now the horizontal axis starts at 10 and runs till 15. 00:10:28.897 --> 00:10:33.563 So some pathogens that are this infectious are things like norovirus. 00:10:33.563 --> 00:10:37.672 If you don't do any hygienic measures, then it's around 14. 00:10:37.672 --> 00:10:40.668 And measles, in the absence of vaccination, 00:10:40.668 --> 00:10:44.063 the reproduction number is between 12 and 18. 00:10:44.063 --> 00:10:47.209 So if nobody is vaccinated and there was one measles case, 00:10:47.209 --> 00:10:51.104 we would expect to see about 15 more measles cases. 00:10:51.104 --> 00:10:55.190 And these are some of the most infectious pathogens that we've got. 00:10:56.010 --> 00:11:00.523 And so here, the line, it really, really is not going to reach 100%. 00:11:00.833 --> 00:11:04.526 It's really not going to get there, no matter how infectious the pathogen, 00:11:04.526 --> 00:11:07.379 which is great news, really good news. 00:11:07.659 --> 00:11:12.725 So, if there was a pathogen that was so infectious like this, 00:11:12.725 --> 00:11:15.713 very infectious, we didn't do anything about it, 00:11:15.713 --> 00:11:20.552 so there were no control measures, there were no interventions, no vaccine, 00:11:20.552 --> 00:11:25.486 and it happened to kill everyone, which is extremely unlikely, 00:11:25.486 --> 00:11:28.836 even then we wouldn't manage to wipe out humanity. 00:11:28.836 --> 00:11:33.660 So to answer that question, no, a pathogen is not going to wipe out humanity. 00:11:33.660 --> 00:11:39.300 Which is really good news for our species, providing of course that the survivors, 00:11:39.300 --> 00:11:43.152 the people who are left over like the look of each other enough 00:11:43.152 --> 00:11:46.087 to repopulate the planet. 00:11:46.087 --> 00:11:48.023 (Laughter) 00:11:48.023 --> 00:11:49.406 So that's good news. 00:11:49.406 --> 00:11:52.152 But normally, and what I do in my work, 00:11:52.152 --> 00:11:55.238 is we don't just try and leave epidemics to happen. 00:11:55.238 --> 00:11:58.598 The goal of my work is to try and understand transmission enough 00:11:58.598 --> 00:12:01.989 in order to develop and evaluate control measures. 00:12:01.989 --> 00:12:03.894 So control measures are things like 00:12:03.894 --> 00:12:08.096 closing schools or encouraging people not to go to work when they're sick 00:12:08.096 --> 00:12:09.982 or vaccinating people. 00:12:09.982 --> 00:12:14.869 And the aim of these control measures is to push that reproduction number, 00:12:14.869 --> 00:12:18.446 the average number of secondary cases, down below one. 00:12:18.586 --> 00:12:23.082 And that's because if each infectious person infects less than one other person, 00:12:23.082 --> 00:12:24.958 the epidemic will decline. 00:12:25.288 --> 00:12:27.716 So that's the goal of my work. 00:12:28.006 --> 00:12:32.326 Now, I do need to tell you about the one exception. 00:12:32.326 --> 00:12:34.844 Because there is always a but to this. 00:12:35.054 --> 00:12:39.920 There is one infection that could be a bit of a problem. 00:12:40.190 --> 00:12:42.868 And it's something that people like to think a lot about, 00:12:42.868 --> 00:12:45.388 and they've even made some movies about. 00:12:45.388 --> 00:12:47.708 And that's zombie infection. 00:12:47.708 --> 00:12:49.029 (Laughter) 00:12:49.029 --> 00:12:51.208 So although it's a bit more light-hearted, 00:12:51.208 --> 00:12:53.293 it's interesting to look at zombie infection 00:12:53.293 --> 00:12:54.663 and figure out why it is 00:12:54.663 --> 00:12:58.553 that this is something that could wipe out everyone on earth. 00:12:58.853 --> 00:13:02.098 So what we'll do is take the same model that we had before. 00:13:02.098 --> 00:13:04.830 We have our susceptible, infectious and recovered groups 00:13:04.830 --> 00:13:06.956 and our rates of transmission. 00:13:06.956 --> 00:13:11.073 And then we have that rate of transmission divided into four parts. 00:13:11.503 --> 00:13:17.949 So why is it that zombie infection could wipe out everybody? 00:13:18.259 --> 00:13:21.301 Well, first of all, zombies break this first rule. 00:13:21.567 --> 00:13:26.134 So, in our model we assume that people recover from infection. 00:13:26.134 --> 00:13:30.237 And as I understand it, nobody recovers from zombie infection. 00:13:30.717 --> 00:13:33.432 There's no films about people who felt sick on the weekend 00:13:33.432 --> 00:13:35.191 but showed up for work on Monday. 00:13:35.191 --> 00:13:36.203 (Laughter) 00:13:36.203 --> 00:13:39.544 The other thing that we assume is that if people die from infection, 00:13:39.544 --> 00:13:43.411 then they stay dead, and zombies don't do that. 00:13:43.411 --> 00:13:44.416 (Laughter) 00:13:44.416 --> 00:13:46.753 So that breaks that rule of our model. 00:13:46.753 --> 00:13:47.747 The other thing is 00:13:47.747 --> 00:13:53.972 that the probability of infection on contact for zombies is very high. 00:13:53.972 --> 00:13:56.484 I gather it is 100%. 00:13:56.484 --> 00:14:00.389 So for something like flu, if you meet an infectious person, it's maybe 10%, 00:14:00.389 --> 00:14:03.877 but for zombies you never see somebody with just a skin wound 00:14:03.877 --> 00:14:05.588 who doesn't get it. 00:14:05.588 --> 00:14:07.312 So it breaks that rule. 00:14:07.312 --> 00:14:09.621 And then finally, remember I told you 00:14:09.621 --> 00:14:13.281 that we assume that people make contacts at random? 00:14:13.281 --> 00:14:16.853 Well, zombies go looking for susceptible people. 00:14:17.743 --> 00:14:19.686 So that breaks that rule. 00:14:19.686 --> 00:14:23.416 And that means that the only epidemic that could really infect everybody 00:14:23.416 --> 00:14:26.630 and wipe out humanity would be a zombie apocalypse. 00:14:26.630 --> 00:14:31.225 And that's really, really good news because zombies are not real. 00:14:31.445 --> 00:14:32.721 Thank you very much. 00:14:32.721 --> 00:14:35.663 (Applause)