Transcriber: 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]