How does maths help in tackling infectious diseases? Understanding how infectious diseases spread involves a lot of maths — to be precise it involves a lot of mathematical modelling. We found this out through our long-standing and fascinating collaboration with the disease modeller Julia Gog of the University of Cambridge.

In this series of very short video clips you can hear from Julia herself as she takes you from the very basic ideas of disease modelling, from the simplest maths right up to what she and her colleagues are working on today. And you can have a go yourself with the lovely interactivities developed by our sister site NRICH, which allow you to explore the ways in which a disease might spread and how these insights feed into mathematical models.

If you've every wondered about the maths that helps us understand the spread of diseases we invite you to join Julia on this accessible introduction to the basics of disease modelling. Whether you're a student keen to know more, a teacher looking to illustrate this fascinating application of mathematics, or just someone who is interested in the maths behind everyday life, we invite you to watch the videos (or read the accompanying text) and play with the interactivities. The project falls into five parts, see the links below.

But first, here's an introduction from Julia.

As Julia explains, she doesn't work alone – she's part of many larger groups who work together, bringing their different approaches together to solve problems in understanding how infectious diseases spread. As well as mathematical modellers, these groups also include scientists from many other disciplines including biology and medicine. "By working together with other disciplines mathematics can make a large contribution to tackling infectious diseases," says Julia. "Possibly at the moment it's not obvious to you how maths can help, but this is exactly what we're going to be exploring together in Contagious Maths."

Part 1: Build your first model — With just some simple arithmetic, you can build a basic mathematical model of how a disease might spread. Julia Gog explains how, and there's also some Lego action...

Part 2: Play Lucky Dip! — You can explore how we might extend our model but running your own epidemic with our Lucky Dip interactivity. Follow along with Julia as she paves the way to a model that is very similar to the mathematics disease modellers use every day.

Part 3: Everybody is different — In Part 3 Julia refines our model to use one of the most important numbers in disease modelling. And there's a chance for you to explore its meaning using a new interactivity.

Part 4: Get moving! — In the final Part we explore what other aspects we need to consider to make a model more realistic. There's an interactivity that allows you to party, commute, and visit friends and we find out more about what life as a research is like from Julia.

Part 5: Meet the researchers! — In this final part, you can meet the researchers themselves and find out about the real research questions that Julia and some of her colleagues are working on!

Relevant reading

You can find more resources that are relevant in our collection Disease modelling for beginners. In particular you might be interested in:

• Maths in a minute: Mathematical models – This article introduces the idea of mathematical models, goes through a simple example, highlights some of the applications that impact our daily lives, and explores why it's important to understand the limitations of our models.
• Maths in a minute: Exponential growth – This introduces the concept of exponential growth, goes through a simple example, and gives you a chance to see the basic maths of exponential growth in action.
• Maths in a minute: R – the reproduction ratio – This easy introduction walks through why the value of R tells us whether we are dealing with an epidemic, and also that it indicates how hard it will be to get the disease under control.
• R and herd immunity – This article extends our explanation of R, explains the link to herd immunity, and shows the basic maths involved in calculating how many people need to be immune to achieve herd immunity.
• Maths in a minute: The SIR model – This article gives a gentle introduction to this important model, that is the basis most disease modellers use to understand the spread of a disease
• How can maths fight an epidemic? – This article explores the role of maths in understanding diseases and what information you need to include to make your models more realistic.

You may also want to see other content we have produced with JUNIPER, a consortium of disease modellers co-led by Julia Gog.

These Contagious Maths resources were developed and written by Julia Gog and the MMP team, including both NRICH and Plus, and funded by the Royal Society’s Rosalind Franklin Award 2020. We have tailored these resources for ages 11-14 on NRICH, and for older students and wider audiences on Plus.