# Mathematics of Epidemics | Trish Campbell | [email protected]

Translator: Yifat Adler

Reviewer: Hussain Laghabi It starts with just one person, and after 8 hours

100 have been infected. 16 hours later, 10,000 people. And a million after the first day. How many people by tomorrow? This is the story of #TheDress. And was it blue and black?

Or was it white and gold? [Laughter] This question was first posed

by a Facebook user who was a family member

of the person who owned the dress. There had been a disagreement

about the color of the dress, and later another user

posted the photo on Tumblr and the rest is history. With over ten million tweets

in the first week, this is an extreme case of going viral. So, let’s take a look at how

#TheDress spreads through a population. The population is divided

into three groups of people. People who haven’t seen the dress, people who have seen

and have started sharing the dress, and people who are

no longer sharing the dress because they’re sick of the dress and never want to hear about it again. And people change groups over time. So, how do the numbers

in each of these groups change? Well, the people who

haven’t seen the dress reduce by the number of people

who start sharing the dress. So, they see it and they start sharing. And the more people that we have sharing, the more new sharers that we get. The people who are sharing the dress increase by the number

of new sharers that we get. But they also decrease by the number

of people who give up sharing. And the people who are

no longer sharing the dress just keep increasing

by the sharers who give up. And we can track what happens to the numbers of people

sharing the dress over time. So, here in a population of ten million. The number of people sharing the dress

starts growing very slowly at first. But then it starts to take off. And once it does so,

it does so very rapidly, and reaches about 4 million people

sharing at any one time up to just a day and a half. Then the numbers fall away to nothing. At the same time, the number of people

who haven’t seen the dress reduces slowly at first and then plummets,

as they start to become new sharers. And the number of people

who are no longer sharing the dress rises really slowly at first

and then it quite reaches its maximum. So, why does the dress stop spreading? Has everybody in the population

seen the dress? Well, no. By the time that

the dress stops spreading, not everybody has seen it. The number of people

who are no longer sharing the dress never quite reaches back up

to a population of ten million. It stops because the people

that are sharing the dress can’t find any new people

to share it with. So they lose interest before they get

to pass it on to anybody else. And, so, the sharing numbers

drop to zero. This is a very simple picture

of how #TheDress spreads in population. And they’ve ignored some realities, like, not everyone has computers

or internet access and not everyone is interested

in sharing memes. So, even if they see it,

they won’t share it. And people have different numbers

of virtual friends. So, it’s not an exact representation, it’s a model, one that is based on

a set of assumptions. So, why should we even care about how a meme spreads through the internet? Well, it turns out that going viral

has its origin in the term virus. So, the way that a meme spreads

through the internet shares many characteristics with the way that an infectious disease

spreads through a real population. So, diseases like Ebola or influenza,

whooping cough, or measles… And fortunately none of these diseases,

or indeed any others known to man, spread any way near as quickly

as #TheDress does through a population. So, while it’s very difficult to stop

a meme such as #TheDress from spreading once it starts going, we’ve got an arsenal of weapons

with which to fight infectious diseases. Vaccines, antibiotics, quarantine,

just to name a few. And a very powerful weapon

behind the scenes: mathematics. Using mathematics to study

infectious diseases isn’t new. A scientist called Daniel Bernoulli

first used probability and statistics nearly 250 years ago to calculate the benefits

of vaccination against smallpox. And the model that I used

to describe the spread of #TheDress has actually been used by epidemiologists

for nearly a hundred years. It’s used to investigate the causes

and spread of infectious diseases and to help develop strategies

to prevent and control them. So, just like we did with #TheDress, we now have a population

that’s made up of people who are susceptible to catch a disease. People who are infectious

and spreading the disease, and people who have recovered

and can no longer pass on the disease. And people will move from these groups. This is called an SIR model, and it’s the basic infectious

disease model. Just like we did with #TheDress, we can keep track of the number of people that are in each

of these groups over time. But just like #TheDress,

we’re also ignoring a lot realities which influence the spread

of infectious diseases. And importantly what we are doing as well

is assuming that everybody in these groups has identical characteristics

and behaviors. And not many diseases or populations

behave quite so simply. So, we often have to allow for

new members to join the population, or for old members to leave. Or we have to account for the fact that for some diseases

just because you’ve had them, it doesn’t mean

that you can’t have them again. And we need to add in vaccination

and treatment for some diseases as well, if we really want to know

how they spread through a population. So, we can run virtual experiments

to answer questions like: how many cases could we prevent

if we had an effective vaccine against Ebola, for example? We can answer questions that

we can’t answer using real people. Sometimes because

the type of experiments that we would need to run

in a population are unethical. And at other times, just because collecting information

is really just too difficult. So, bear in mind that when these models were

first developed a hundred years ago, all the calculations

would have been done by hand. So, increasing computational power,

though, has meant that the process of mathematically modeling

infectious diseases has got much much faster, and we can now add

a lot more data into models to try and build a match

what’s really happening in a population. So, in this era of big data with rapid advances

in science and technology, we are seeing a rapid evolution in

the field of infectious disease modelling. So, here is just a few of the things

that are happening. We now have individual base models which follow the history

of individuals in a population and track the information that changes

their chance of catching a disease. So, things like their infection history,

their vaccination history, the number and ages of people

that they live with. People are even now using

radio frequency identification tags to start collecting information

on how people contact other people, how they move through a population. Because how you mix with

other members of a population is very important

to the spread of infectious disease. So, we’ve gone from modeling

groups of people in a population to modeling individual characteristics

and behaviors of individuals, to modeling the genomes,

the genetic material of the organisms that actually cause disease,

viruses and bacteria. And we are doing that so we can

find out who patient zero was, and to look at how the infection

has spread through a population. And we’re also using mathematics

to investigate how infectious diseases,

viruses and bacteria actually spread within a human body, and how our immune system

is fighting back. And all of this work is hoping

to give us a better understanding of how infectious diseases spread

and how we can stop them. In my lifetime, we’ve seen

the eradication of smallpox. And we’re on track to see

the eradication of polio in yours. Through careful planning aided by

the use of mathematical models, we wipe diseases that have caused millions of deaths

off the face of the Earth. But infectious diseases isn’t

the only application of mathematics to health problems. There are many biological processes

that are still a mystery and lend themselves

to mathematical exploration. So, what questions will you

answer using mathematics? Thank you.

[Applause]