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One hundred years ago,
a new influenza virus emerged,

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spread around the world
and killed 50 to 100 million people.

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For every 40 people that got
this influenza infection,

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one of them died.

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And you think, maybe
that's not that bad odds,

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but for the most recent
influenza pandemic,

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for each person that died
there were probably 10,000 cases.

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Which means that
this 1918 influenza pandemic

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was the worst pandemic in history.

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Here's a graph showing the weekly deaths
at the time of the pandemic

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in New York, London, Paris and Berlin.

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You can quite clearly see in the middle,
the major wave of the pandemic.

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And so all the way
from North America to Europe,

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this pandemic was happening
at the same time.

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And this synchronicity, this is 
a common feature of influenza pandemics.

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So not only was there this major
influenza pandemic in 1918,

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but it was also the tail end
of the First World War.

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And I've marked here the Armistice,

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so the official end
of the First World War, in white.

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So you can see here that not only
was this a terrible time for Europe,

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but data were being collected on deaths.

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And this really showed
that infectious diseases are a priority

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and that we need
to collect these kind of data

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to understand how and why
these epidemics happen.

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So computational and mathematical tools
can be used on data like these

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to understand the transmission processes
and how the epidemic is occurring

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with the ultimate aim of trying to develop
interventions, so control methods,

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to curtail the epidemic
and to slow down transmission.

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So, the difference between epidemics
and pandemics is one of scale.

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Since they're Greek words,
you probably already know them,

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but for those who aren't,
I'll just briefly explain.

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An epidemic is geographically
localized to one place.

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So for instance, the recent Ebola epidemic
in West Africa was confined to West Africa

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and is therefore an epidemic.

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The 1918 influenza pandemic,
that spread around the world.

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And spreading around the world
is what defines a pandemic.

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When we get any new epidemic,
one thing that we're really interested in

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is how quickly it's spreading
from person to person.

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And we define this
as the reproduction number.

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So the reproduction number
is the average number of new cases

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that each infectious person
causes at the start.

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So if you were the first person

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that got an epidemic,
or got a new virus or a new pathogen,

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and nobody else had had it,
how many people would you infect?

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So let's take, for example, that
one infectious person walks into the room.

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And if the reproduction number is two,
we expect two new cases from that person.

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And if those two people go off
and infect two more of their friends,

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well, they might not have
two friends anymore,

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but we now have four cases.

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And then if those four infect
two more each and so on and so forth,

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you can see that the epidemic will grow.

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So the reproduction number,

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the average number of people
that each infectious person infects,

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really determines how quickly
the epidemic grows.

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OK, well, this is true,
especially in the beginning.

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But, if you carried on like this
with each person infecting two,

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step by step, as we've shown here,

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by the 33rd step, you would have
infected everybody on earth.

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And we know that that doesn't happen.

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So, why is it that that doesn't happen?

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Well, this is because you start
to run out of susceptible people,

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so people who haven't had the infection,

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and this is called
depletion of susceptibles.

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So, to demonstrate this,
let's imagine that this person here,

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we'll call her Christina,

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Christina was infected in the second step,

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which seems like pretty bad luck.

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Christina happens to be
friends with Spyros.

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So when Spyros gets infected later,
and he tries to infect two more,

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one of the people
he tries to infect is Christina.

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But she's already had it.

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So here she is colored in blue because
she's has got immunity to infection

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now that she's recovered.

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So when Spyros tries
to infect her, he can't,

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and that means that
the number infected slows down.

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And if this is true for other people
in the population, like this,

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then you start to see a slow down
in the number of people infected.

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So this is depletion of susceptibles.

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And I'll show you how we incorporate
these kind of processes

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into models of transmission.

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If we were going to model
something like flu,

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the first thing we would do
is divide the population

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into three disease groups.

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So here you can see people
who are susceptible to infection,

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so they're able to get infected.

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You can see infectious people
who have got the infection

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and are spreading it to other people.

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And then you've got in blue
the recovered or died group.

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So normally we assume
that when people recover from infection,

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they are protected.

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But if it's a very severe infection,
they may also have died.

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And everybody in the population
has to be one of these groups.

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And we determine the rates
of transition between each group.

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So when you get infected,
this happens at the rate of transmission,

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and then when people recover,
this happens at the rate of recovery.

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So this rate of transmission
is the most important one

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when we're thinking about
how quickly epidemics grow.

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What we want to define is when you have
an infectious person in the population

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and they go out and they make
contacts with the people that they know,

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how likely are they to pass
that infection on to their contacts?

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And so, what we do when we mathematically
define the rate of transmission

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is we're going
to divide it into four parts.

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So first of all, we have
our rate of transmission

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is equal to the number
of infectious people.

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So the more infectious people there are,

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the higher the rate
of transmission will be

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because there's a lot of people
around infecting people.

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Then we multiply it by the number of
contacts that each person has on average.

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So you can see here that the infectious
people make those contacts at random

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with susceptible, infectious
or recovered people.

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Then we include the probability
of infection on a contact.

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So what is the chance

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that when an infectious person
meets a susceptible person

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they give them the infection?

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For flu, this is probably around 10%,
something like that.

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And then finally, we include
the proportion of the population

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who are susceptible.

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So at the beginning of an epidemic,
when most people are susceptible,

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so they haven't had it,

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the probability that you meet
a susceptible person is quite high.

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But later, as this pool is depleted,
so you run out of susceptible people,

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it becomes less likely
that you'll meet a susceptible individual.

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So let's see how this
is incorporated into our models.

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So this is what an epidemic looks like -

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a simulated epidemic in 5,000 people.

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You can see the grey bar
marks the susceptible group,

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and it starts at 5,000,
which is everybody,

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apart from one infectious person
at the beginning.

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In red you can the infectious epidemic,

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and then in blue,
the recovered group at the end.

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So what you might notice
is that at this point,

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when half of the susceptible
individuals have been infected,

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this part of the equation,
the proportion of the susceptible,

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is also halved,

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which really pushes down
the rate of transmission.

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And that's important, because
it's this depletion of susceptibles,

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so running out of susceptible people,

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that causes the epidemic
to peak and then decline.

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Now, the eagle-eyed among you
might have also noticed

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that if you draw a horizontal line
at 5,000, which is the total population,

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that by the end of the epidemic
there's a small gap.

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There's a gap between
the total number of susceptible people

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and the number of people
that were infected in total.

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And that's because some people
don't get infected.

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The lucky ones.

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So this total number of people infected
and the size of the gap

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is determined by the reproduction number,
by how infectious the pathogen is.

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So let's explore
how that relationship looks.

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So what I'm showing you here,

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on the horizontal axis you can see
reproduction numbers from zero to five.

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And on the vertical axis you can see
the percent of the population

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that are infected in total.

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So let's take a look at some pathogens
that you might have heard of

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and see what their
reproduction numbers are.

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So here, for example, seasonal influenza,
probably around 1.4-1.5.

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Ebola, that's around 2.

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Pandemic flu, maybe 2.5.

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SARS, around 3.

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And then smallpox, around 5.

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So for every case of smallpox
that we could see in the population,

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we would expect to see
five more smallpox cases.

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So, what's the relationship?

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Here you can see that from zero to one,

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when the reproduction number
is less than one,

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nobody is infected.

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And that's because if you infect
less than one person

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for each infectious person,
there's no epidemic.

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And then it takes off rapidly,

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and it appears to approach 100%.

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But it doesn't quite.

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That line doesn't quite reach 100%.

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And to show you that, let's take a look
at even higher reproduction numbers.

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So here you can see the same graph,

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but now the horizontal axis
starts at five and runs till 10,

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and the vertical axis is much higher.

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So some pathogens in this region are
pertussis, which causes whooping cough,

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and polio and diphtheria
are also around here.

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So again you see the line increases
as the reproduction number gets higher.

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But it still doesn't reach 100%
even though it looks like it.

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OK, so what about if
it's even, even higher than that?

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So let's take a look now, the same graph,

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but now the horizontal axis
starts at 10 and runs till 15.

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So some pathogens that are this infectious
are things like norovirus.

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If you don't do any hygienic measures,
then it's around 14.

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And measles, in
the absence of vaccination,

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the reproduction number
is between 12 and 18.

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So if nobody is vaccinated
and there was one measles case,

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we would expect to see
about 15 more measles cases.

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And these are some of the most
infectious pathogens that we've got.

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And so here, the line, it really, really
is not going to reach 100%.

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It's really not going to get there,
no matter how infectious the pathogen,

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which is great news, really good news.

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So, if there was a pathogen
that was so infectious like this,

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very infectious,
we didn't do anything about it,

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so there were no control measures,
there were no interventions, no vaccine,

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and it happened to kill everyone,
which is extremely unlikely,

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even then we wouldn't manage
to wipe out humanity.

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So to answer that question, no, a pathogen
is not going to wipe out humanity.

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Which is really good news for our species,
providing of course that the survivors,

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the people who are left over
like the look of each other enough

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to repopulate the planet.

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(Laughter)

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So that's good news.

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But normally, and what I do in my work,

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is we don't just try
and leave epidemics to happen.

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The goal of my work is to try
and understand transmission enough

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in order to develop
and evaluate control measures.

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So control measures are things like

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closing schools or encouraging people
not to go to work when they're sick

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or vaccinating people.

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And the aim of these control measures
is to push that reproduction number,

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the average number of secondary
cases, down below one.

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And that's because if each infectious
person infects less than one other person,

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the epidemic will decline.

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So that's the goal of my work.

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Now, I do need to tell you
about the one exception.

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Because there is always a but to this.

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There is one infection
that could be a bit of a problem.

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And it's something that people
like to think a lot about,

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and they've even made some movies about.

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And that's zombie infection.

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(Laughter)

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So although it's a bit more light-hearted,

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it's interesting to look
at zombie infection

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and figure out why it is

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that this is something that
could wipe out everyone on earth.

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So what we'll do is take
the same model that we had before.

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We have our susceptible, infectious
and recovered groups

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and our rates of transmission.

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And then we have that rate of transmission
divided into four parts.

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So why is it that zombie infection
could wipe out everybody?

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Well, first of all,
zombies break this first rule.

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So, in our model we assume
that people recover from infection.

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And as I understand it,
nobody recovers from zombie infection.

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There's no films about people
who felt sick on the weekend

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but showed up for work on Monday.

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(Laughter)

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The other thing that we assume is
that if people die from infection,

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then they stay dead,
and zombies don't do that.

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(Laughter)

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So that breaks that rule of our model.

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The other thing is

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that the probability of infection
on contact for zombies is very high.

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I gather it is 100%.

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So for something like flu, if you meet
an infectious person, it's maybe 10%,

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but for zombies you never see
somebody with just a skin wound

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who doesn't get it.

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So it breaks that rule.

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And then finally, remember I told you

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that we assume that people
make contacts at random?

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Well, zombies go looking
for susceptible people.

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So that breaks that rule.

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And that means that the only epidemic
that could really infect everybody

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and wipe out humanity
would be a zombie apocalypse.

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And that's really, really good news
because zombies are not real.

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Thank you very much.

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(Applause)