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]