- Snapshots of modern mathematics
- Pierre de Fermat and Andrew Wiles in Czech Republic stamps
- Stefan Banach (March 30, 1892 – August 8, 1945)
- Guessing the Numbers
- What is mathematics for Ehrhard Behrends
- What is mathematics for Krzysztof Ciesielski
- The Three Ducks Trick
- What is mathematics for Franka Brueckler

# Plus Magazine Monthly Column – November 2017 – Part II: Preventing Pandemics

*Plus http://plus.maths.org is a free online magazine about mathematics aimed at a general audience. It is part of the Millennium Mathematics Project, based at the University of Cambridge and our aim is to open a door onto the world of maths for everyone. We run articles, videos and podcasts on all aspect of mathematics, from pure maths and theoretical physics to mathematical aspects of art, medicine, cosmology, sport and more. Plus has a news section, covering news from the world of maths as well as the maths behind the mainstream news, reviews of books, plays and films, as well as puzzles for you to sharpen your wits.*

**Preventing pandemics**

It’s very possible that at this particular moment you don’t feel able to engage with complex things like the horseshoe map because you have a flu and your head isn’t working. While your flu is hopefully going to pass in a few days, others aren’t so lucky. During the pandemic in 2009 over 60 million people caught the H1N1 influenza virus in the United States: over 274,000 of these required hospital and, sadly, over 12,000 people died.

Julia Gog, a mathematician at the University of Cambridge, has been researching the spread of infectious diseases for years. Now her and her team have teamed up with the BBC on an innovative project, BBC Pandemic, combining outreach, citizen science and new mathematical research, to gather much-needed data.

“Our motivation for doing this is to build better models for [disease] spread in the UK,” says Gog. Any UK resident can contribute to the data collection via the BBC Pandemic app on their smartphone (via the App Store or Google Play).

“The immediate outcome will be running some simulations of pandemics for a programme for BBC 4, which will be broadcast in early 2018,” says Gog “But the other part is we will be collecting the data so we can study it, and [the data] will be available to other scientists. The point is to understand how people move, as we want to make better models for pandemics and other infectious disease [outbreaks].”

When modelling how a disease spreads, says Gog, you want your models to be tractable, and simple enough so you can understand what’s gone into them. “But the temptation is just to put in more and more detail, and then you’ve got to model how everyone moves.”

It’s easier to use models that are more transparent, and that you can run quickly and repeatedly. “The project we have been working on for the last few years is based on [data] from the 2009 pandemic of an influenza-like illness in the US.” Here, rather than modelling how the disease spreads between individuals in the population, Gog and her colleagues model how diseases spread between larger units representing cities, towns or villages. These models are based on movement between these city (or town or village) units, which depend on the distance between them, their size and their proximity to other large cities.

Gog and her colleagues have been using the 2009 data to infer the movement patterns between city units. There are not many data sets that specifically gather this movement data. Those that do exist, some collected by apps and some by surveys, are not on the scale the BBC Pandemic project promises and do not connect the information in this way. “We don’t think any other studies will be comparable to this one, and certainly not in the UK.”

“The big one for us is that this data set will be available to all scientists. I don’t know anything like it,” says Gog. “They can have all of it!” Thanks to the careful way the data is collected, anonymised and shared, and the permissions for its use that are gathered through the app, it will be the first time such a data set will be made available like this. There is already a great deal of interest from other scientists who were not expecting to have such access to the data. Early on in the project Gog and her colleagues will write a paper to show how the data was gathered, how it is valid, and to encourage other scientists to use the BBC Pandemic dataset.

It is inevitable that another pandemic will strike, and research like this will help governments decide the best response, whether it is closing schools or issuing vaccines. And through innovative projects like this, everyone can help fight the threat posed by influenza and other highly infectious diseases.

**Complex numbers: Why we love them**

In 1940 a minor gale hit the Tacoma Narrows Bridge in Washington State, which started swinging as a result and eventually collapsed — dramatically.

It’s the task of engineers to prevent these kind of disasters, and engineers obviously use mathematics. But what’s particularly nice about this example — if you’re a maths educator or communicator, not the poor dog that was trapped in a car on the bridge — is that to prevent bridges being driven to collapse by oscillation, engineers use complex numbers. Complex numbers are one of the first topics you encounter if you study maths past the basic high school level. They are fascinating in their own right, symbolising the mathematical bravery needed to transgress boundaries and discover new mathematical worlds. But what’s often missing from the teaching are the applications of complex numbers. The Tacoma Bridge provides a great example of such an application.

And there are many more. “Many different waves, whether it’s [waves from] electricity, sound, or light [are described by sine waves],” explains Chris Budd, Professor of Applied Mathematics at the University of Bath. “To do all those calculations [involving] sine waves can get really complicated, but there’s a brilliant shortcut involving complex numbers.”

That shortcut is of course Euler’s famous identity,

$$e^{i\theta} = \cos{\theta} + i \sin{\theta},$$

which makes calculations using waves a whole lot easier. And so it is that complex numbers not only keep bridges from collapsing, but also keep alternating current running to your house to keep the lights on at all times.

We recently produced an introductory package of articles and videos on *Plus*, dedicated to the uses of complex numbers within and outside of mathematics. It contains videos featuring Budd, engineer Ahmer Wadee and complex dynamicist Holly Krieger, as well as articles about the uses of complex numbers, including their uses in movies, the famous Mandelbrot set, and a bit of history. If you’re someone who’d like to impress the beauty and usefulness of complex numbers on an unsuspecting general audience, this content might provide some contextual glue.

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