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)

## 3 Comments

Awesome news! Except on the poisonous vaccines with questionable ingredients!

*gulp*This lecture has now become more pertinent in light of the recent outbreak of the COVID-19 virus.