100 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
shows that infectious diseases are a
priority and 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 their
Greek words you probably already know
them but for those who 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 it’s therefore an epidemic
the 1918 influenza pandemic that spread
around the world and spreading around
the world is what defines the pandemic
when we get any new epidemic one thing
we’re really interested in is how
quickly it spread
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 others 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 2 we expect two
new cases from that person and if those
2 people go off and in fact 2 more of
their friends well they might not have 2
friends anymore but we now have 4 cases
and then if those 4 infect 2 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 2 step by step as we 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
Cristina Cristina was infected in the
second step which seems like pretty bad
luck Cristina happens to be friends with
spirits
so when Sparrow’s gets infected later
and he tries to infect two more one of
the people he tries to infect it’s
Cristina but she’s already had it so
here she is colored in blue because she
has got immunity to infection now that
she’s recovered so when Spiros 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 slowdown in the number of people
infected so this is depletion of
susceptibles and I’ll show you how we
incorporate the
kind of processes into models of
transmission so 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
infections so they’re able to get
infected you can see infectious people
who have got the infection are spreading
it to other people and then you’ve got
in blue they’re recovered or died group
so normally we assume that when people
recover from infection they’re 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 that
translate through 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 and 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 infecting
people then we multiply it by the number
of contacts that each person has on
average so you can see here that the per
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 an
acceptable 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 into our model
so this is what an epidemic looks like a
simulated epidemic in five thousand
people you can see the gray bar marks
the susceptible group and it starts at
five thousand which is everybody apart
from one infectious person at the
beginning in red you can see 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 half which really pushes down the
rate of transmission and that’s
important because it’s this depletion of
susceptible 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 five thousand 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 the 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 –
pandemic flu maybe two and a half SARS
around three and then small part
around 5:00 so for every case of
smallpox that we see 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
0 to 1 when the reproduction number is
less than 1
there’s no 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 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 5 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 okay 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 and
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 this really 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 they have
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 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 those
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
in fact less than one other person the
epidemic will decline so that’s the goal
of 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 so although it’s a bit
more lighthearted 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 transition and
then we have that rate of transmission
divided into four parts so why is it
that zombies that zombie infection could
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
you don’t hear there’s no films about
people who felt sick on the weekend but
showed up for work on Monday
the other thing that we assume is that
if people die from infection then they
stay dead and zombies don’t do that
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 percent
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 people
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]
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
shows that infectious diseases are a
priority and 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 their
Greek words you probably already know
them but for those who 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 it’s therefore an epidemic
the 1918 influenza pandemic that spread
around the world and spreading around
the world is what defines the pandemic
when we get any new epidemic one thing
we’re really interested in is how
quickly it spread
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 others 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 2 we expect two
new cases from that person and if those
2 people go off and in fact 2 more of
their friends well they might not have 2
friends anymore but we now have 4 cases
and then if those 4 infect 2 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 2 step by step as we 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
Cristina Cristina was infected in the
second step which seems like pretty bad
luck Cristina happens to be friends with
spirits
so when Sparrow’s gets infected later
and he tries to infect two more one of
the people he tries to infect it’s
Cristina but she’s already had it so
here she is colored in blue because she
has got immunity to infection now that
she’s recovered so when Spiros 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 slowdown in the number of people
infected so this is depletion of
susceptibles and I’ll show you how we
incorporate the
kind of processes into models of
transmission so 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
infections so they’re able to get
infected you can see infectious people
who have got the infection are spreading
it to other people and then you’ve got
in blue they’re recovered or died group
so normally we assume that when people
recover from infection they’re 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 that
translate through 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 and 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 infecting
people then we multiply it by the number
of contacts that each person has on
average so you can see here that the per
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 an
acceptable 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 into our model
so this is what an epidemic looks like a
simulated epidemic in five thousand
people you can see the gray bar marks
the susceptible group and it starts at
five thousand which is everybody apart
from one infectious person at the
beginning in red you can see 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 half which really pushes down the
rate of transmission and that’s
important because it’s this depletion of
susceptible 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 five thousand 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 the 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 –
pandemic flu maybe two and a half SARS
around three and then small part
around 5:00 so for every case of
smallpox that we see 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
0 to 1 when the reproduction number is
less than 1
there’s no 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 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 5 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 okay 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 and
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 this really 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 they have
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 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 those
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
in fact less than one other person the
epidemic will decline so that’s the goal
of 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 so although it’s a bit
more lighthearted 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 transition and
then we have that rate of transmission
divided into four parts so why is it
that zombies that zombie infection could
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
you don’t hear there’s no films about
people who felt sick on the weekend but
showed up for work on Monday
the other thing that we assume is that
if people die from infection then they
stay dead and zombies don’t do that
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 percent
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 people
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]
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