Transcriber: Chryssa R. Takahashi
Reviewer: Rhonda Jacobs One hundred years ago,
a new influenza virus emerged, spread around the world
and killed 50 to 100 million people. For every 40 people that got
this influenza infection, one of them died. And you think, maybe
that's not that bad odds, but for the most recent
influenza pandemic, for each person that died
there were probably 10,000 cases. Which means that
this 1918 influenza pandemic was the worst pandemic in history. Here's a graph showing the weekly deaths
at the time of the pandemic in New York, London, Paris and Berlin. You can quite clearly see in the middle,
the major wave of the pandemic. And so all the way
from North America to Europe, this pandemic was happening
at the same time. And this synchronicity, this is
a common feature of influenza pandemics. So not only was there this major
influenza pandemic in 1918, but it was also the tail end
of the First World War. And I've marked here the Armistice, so the official end
of the First World War, in white. So you can see here that not only
was this a terrible time for Europe, but data were being collected on deaths. And this really showed
that infectious diseases are a priority and that we need
to collect these kind of data to understand how and why
these epidemics happen. So computational and mathematical tools
can be used on data like these to understand the transmission processes
and how the epidemic is occurring with the ultimate aim of trying to develop
interventions, so control methods, to curtail the epidemic
and to slow down transmission. So, the difference between epidemics
and pandemics is one of scale. Since they're Greek words,
you probably already know them, but for those who aren't,
I'll just briefly explain. An epidemic is geographically
localized to one place. So for instance, the recent Ebola epidemic
in West Africa was confined to West Africa and is therefore an epidemic. The 1918 influenza pandemic,
that spread around the world. And spreading around the world
is what defines a pandemic. When we get any new epidemic,
one thing that we're really interested in is how quickly it's spreading
from person to person. And we define this
as the reproduction number. So the reproduction number
is the average number of new cases that each infectious person
causes at the start. So if you were the first person that got an epidemic,
or got a new virus or a new pathogen, and nobody else had had it,
how many people would you infect? So let's take, for example, that
one infectious person walks into the room. And if the reproduction number is two,
we expect two new cases from that person. And if those two people go off
and infect two more of their friends, well, they might not have
two friends anymore, but we now have four cases. And then if those four infect
two more each and so on and so forth, you can see that the epidemic will grow. So the reproduction number, the average number of people
that each infectious person infects, really determines how quickly
the epidemic grows. OK, well, this is true,
especially in the beginning. But, if you carried on like this
with each person infecting two, step by step, as we've shown here, by the 33rd step, you would have
infected everybody on earth. And we know that that doesn't happen. So, why is it that that doesn't happen? Well, this is because you start
to run out of susceptible people, so people who haven't had the infection, and this is called
depletion of susceptibles. So, to demonstrate this,
let's imagine that this person here, we'll call her Christina, Christina was infected in the second step, which seems like pretty bad luck. Christina happens to be
friends with Spyros. So when Spyros gets infected later,
and he tries to infect two more, one of the people
he tries to infect is Christina. But she's already had it. So here she is colored in blue because
she's has got immunity to infection now that she's recovered. So when Spyros tries
to infect her, he can't, and that means that
the number infected slows down. And if this is true for other people
in the population, like this, then you start to see a slow down
in the number of people infected. So this is depletion of susceptibles. And I'll show you how we incorporate
these kind of processes into models of transmission. If we were going to model
something like flu, the first thing we would do
is divide the population into three disease groups. So here you can see people
who are susceptible to infection, so they're able to get infected. You can see infectious people
who have got the infection and are spreading it to other people. And then you've got in blue
the recovered or died group. So normally we assume
that when people recover from infection, they are protected. But if it's a very severe infection,
they may also have died. And everybody in the population
has to be one of these groups. And we determine the rates
of transition between each group. So when you get infected,
this happens at the rate of transmission, and then when people recover,
this happens at the rate of recovery. So this rate of transmission
is the most important one when we're thinking about
how quickly epidemics grow. What we want to define is when you have
an infectious person in the population and they go out and they make
contacts with the people that they know, how likely are they to pass
that infection on to their contacts? And so, what we do when we mathematically
define the rate of transmission is we're going
to divide it into four parts. So first of all, we have
our rate of transmission is equal to the number
of infectious people. So the more infectious people there are, the higher the rate
of transmission will be because there's a lot of people
around infecting people. Then we multiply it by the number of
contacts that each person has on average. So you can see here that the infectious
people make those contacts at random with susceptible, infectious
or recovered people. Then we include the probability
of infection on a contact. So what is the chance that when an infectious person
meets a susceptible person they give them the infection? For flu, this is probably around 10%,
something like that. And then finally, we include
the proportion of the population who are susceptible. So at the beginning of an epidemic,
when most people are susceptible, so they haven't had it, the probability that you meet
a susceptible person is quite high. But later, as this pool is depleted,
so you run out of susceptible people, it becomes less likely
that you'll meet a susceptible individual. So let's see how this
is incorporated into our models. So this is what an epidemic looks like - a simulated epidemic in 5,000 people. You can see the grey bar
marks the susceptible group, and it starts at 5,000,
which is everybody, apart from one infectious person
at the beginning. In red you can the infectious epidemic, and then in blue,
the recovered group at the end. So what you might notice
is that at this point, when half of the susceptible
individuals have been infected, this part of the equation,
the proportion of the susceptible, is also halved, which really pushes down
the rate of transmission. And that's important, because
it's this depletion of susceptibles, so running out of susceptible people, that causes the epidemic
to peak and then decline. Now, the eagle-eyed among you
might have also noticed that if you draw a horizontal line
at 5,000, which is the total population, that by the end of the epidemic
there's a small gap. There's a gap between
the total number of susceptible people and the number of people
that were infected in total. And that's because some people
don't get infected. The lucky ones. So this total number of people infected
and the size of the gap is determined by the reproduction number,
by how infectious the pathogen is. So let's explore
how that relationship looks. So what I'm showing you here, on the horizontal axis you can see
reproduction numbers from zero to five. And on the vertical axis you can see
the percent of the population that are infected in total. So let's take a look at some pathogens
that you might have heard of and see what their
reproduction numbers are. So here, for example, seasonal influenza,
probably around 1.4-1.5. Ebola, that's around 2. Pandemic flu, maybe 2.5. SARS, around 3. And then smallpox, around 5. So for every case of smallpox
that we could see in the population, we would expect to see
five more smallpox cases. So, what's the relationship? Here you can see that from zero to one, when the reproduction number
is less than one, nobody is infected. And that's because if you infect
less than one person for each infectious person,
there's no epidemic. And then it takes off rapidly, and it appears to approach 100%. But it doesn't quite. That line doesn't quite reach 100%. And to show you that, let's take a look
at even higher reproduction numbers. So here you can see the same graph, but now the horizontal axis
starts at five and runs till 10, and the vertical axis is much higher. So some pathogens in this region are
pertussis, which causes whooping cough, and polio and diphtheria
are also around here. So again you see the line increases
as the reproduction number gets higher. But it still doesn't reach 100%
even though it looks like it. OK, so what about if
it's even, even higher than that? So let's take a look now, the same graph, but now the horizontal axis
starts at 10 and runs till 15. So some pathogens that are this infectious
are things like norovirus. If you don't do any hygienic measures,
then it's around 14. And measles, in
the absence of vaccination, the reproduction number
is between 12 and 18. So if nobody is vaccinated
and there was one measles case, we would expect to see
about 15 more measles cases. And these are some of the most
infectious pathogens that we've got. And so here, the line, it really, really
is not going to reach 100%. It's really not going to get there,
no matter how infectious the pathogen, which is great news, really good news. So, if there was a pathogen
that was so infectious like this, very infectious,
we didn't do anything about it, so there were no control measures,
there were no interventions, no vaccine, and it happened to kill everyone,
which is extremely unlikely, even then we wouldn't manage
to wipe out humanity. So to answer that question, no, a pathogen
is not going to wipe out humanity. Which is really good news for our species,
providing of course that the survivors, the people who are left over
like the look of each other enough to repopulate the planet. (Laughter) So that's good news. But normally, and what I do in my work, is we don't just try
and leave epidemics to happen. The goal of my work is to try
and understand transmission enough in order to develop
and evaluate control measures. So control measures are things like closing schools or encouraging people
not to go to work when they're sick or vaccinating people. And the aim of these control measures
is to push that reproduction number, the average number of secondary
cases, down below one. And that's because if each infectious
person infects less than one other person, the epidemic will decline. So that's the goal of my work. Now, I do need to tell you
about the one exception. Because there is always a but to this. There is one infection
that could be a bit of a problem. And it's something that people
like to think a lot about, and they've even made some movies about. And that's zombie infection. (Laughter) So although it's a bit more light-hearted, it's interesting to look
at zombie infection and figure out why it is that this is something that
could wipe out everyone on earth. So what we'll do is take
the same model that we had before. We have our susceptible, infectious
and recovered groups and our rates of transmission. And then we have that rate of transmission
divided into four parts. So why is it that zombie infection
could wipe out everybody? Well, first of all,
zombies break this first rule. So, in our model we assume
that people recover from infection. And as I understand it,
nobody recovers from zombie infection. There's no films about people
who felt sick on the weekend but showed up for work on Monday. (Laughter) The other thing that we assume is
that if people die from infection, then they stay dead,
and zombies don't do that. (Laughter) So that breaks that rule of our model. The other thing is that the probability of infection
on contact for zombies is very high. I gather it is 100%. So for something like flu, if you meet
an infectious person, it's maybe 10%, but for zombies you never see
somebody with just a skin wound who doesn't get it. So it breaks that rule. And then finally, remember I told you that we assume that people
make contacts at random? Well, zombies go looking
for susceptible people. So that breaks that rule. And that means that the only epidemic
that could really infect everybody and wipe out humanity
would be a zombie apocalypse. And that's really, really good news
because zombies are not real. Thank you very much. (Applause)
