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)