Contagious Maths: Bringing maths research into the classroom

Marianne Freiberger Share this page

We're proud to announce the launch of a school curriculum and public engagement project developed in collaboration with mathematical biologist Julia Gog and our sister site NRICH! Contagious Maths is a hands-on exploration of disease modelling, featuring video clips and web-based interactivities and requiring no previous knowledge of the area. The project consists of two strands, one aimed at a general self-guided audience and published here on Plus and the other aimed at school students aged 11 to 14 and their teachers, published on the NRICH site.

The project is supported by a Royal Society Rosalind Franklin Award grant, which Gog won in 2020. The prize is awarded annually and comes with a grant of £40,000 to implement a project to raise the profile of women in STEM.

"The 11-14 age we are targeting is a real crunch point for retaining girls in maths, and future female mathematicians," Gog said in an interview on the Royal Society website. "What exactly happens is complex and multifaceted, but this is a period when people form their views on how they fit with maths and science. Many disengage as it can seem that 'maths' at school is utterly disconnected from the real world. It can also be a time when maths appears very starkly right or wrong, whereas any research mathematician can tell you it's always so much more subtle than that, and therefore so much more interesting!"

From 2 times 2 to research maths

The dynamic nature of mathematical modelling, and mathematical research generally, is central to Contagious Maths. In a sequence of short video clips Gog encourages users to investigate topics such as exponential growth, the reproduction ratio R, and herd immunity, and gently guides her audience towards the idea of a mathematical model.


This photo shows Julia Gog (middle), Plus Editor Marianne Freiberger (left) and Howard France (right) of video production company Avito Ltd during a shoot for the Contagious Maths project.

Interactivities allow users to explore these ideas for themselves. The Lucky Dip interactivity, for example, uses a tombola to simulate the outbreak of an epidemic, with infected 'individuals' being picked at random from a population and going on to infect others. Users can change the corresponding value of R and observe differences and similarities between runs of the simulated epidemic (you can play with the interactivity below).

Underlying this interactivity, as Gog explains in one of the video clips, is the so-called SIR model, a leading paradigm in epidemiology. Contagious Maths provides a playful and intuitive introduction to the mathematical ideas behind the model without recourse to sophisticated equations, while always referencing the reality of mathematical modelling. "We've been frank that the maths is never black and white in this field, there are always ways to challenge and develop the models, and some tricky thinking to be done about how the real epidemics and the simulations are really related to each other," Gog said in the Royal Society interview.

The suite of resources falls into five parts, or lessons, with ample guidance for teachers provided on the NRICH site. "We're also arming teachers with the ideas and tools to do this, so they have at their fingertips all they need to deliver these lessons. Maybe those teachers have no experience of research mathematics. We hope this project will help these teachers to bring in the wider view of mathematics, and we hope it inspires them too."

The sequence of lessons is rooted in the mathematics curriculum, but while it starts with the simple idea of repeated multiplication, it ends with users exploring the kind of questions professional epidemiologists try to answer in their work. The project also brings in some of Gog's colleagues, culminating in a sequence of short video clips featuring Gog talking about her research into optimal allocation of vaccine doses, Petra Klepac explaining the importance of contact patterns in epidemiology, and PhD students Maria Alegria Gutierrez and Desmond Lai talking about their work on virus mutation and waning immunity.

Combining forces

Gog is Professor of Mathematical Biology here at the Department of Applied Mathematics and Theoretical Physics (DAMTP), which is also the home of Plus. With research focussing on disease modelling, Gog played a vital role in the UK's response to the COVID-19 pandemic. She contributed to the Scientific Advisory Group for Emergencies (SAGE) and the Scientific Pandemic Influenza Group on Modelling (SPI-M), and earned an OBE for her work.

Gog also has a long-standing interest in communicating mathematics to wider audiences. Over the years she has worked closely with the Millennium Mathematics Project (MMP), of which both Plus and NRICH are a part, and became the MMP's Director in 2023. Gog's work in outreach and public engagement includes the UK's largest citizen science project, delivered in 2018 in collaboration with the BBC, and co-presenting the 2021 Royal Institution Christmas Lecture.


As you'll learn in Contagious Maths, contact patterns are all important in epidemiology.

During the COVID-19 pandemic, Gog co-founded a consortium of disease modellers called JUNIPER. We, the Editors of Plus, were invited to join JUNIPER, tasked with communicating its members' research to wider audiences. We're proud to have received an award from SAGE for this work. You can see the relevant content here.

Contagious Maths draws on Gog's expertise in disease modelling and communication, as well as the strengths of the MMP's projects: communicating mathematical research to wider audiences, which is what we do here at Plus, and developing inspiring resources for schools, the remit of NRICH.

The aim is, not just to bring across the excitement of mathematics and the benefits it has for society, but also to introduce some of the people who make the maths. "Visible role models can make pursuing STEM seem more imaginable to more school students, and help them decide they want to pursue it," said Gog. "It’s a matter of fairness, everyone should have these wonderful opportunities, but it also benefits STEM. New students are our lifeblood, and we want those who can bring the most in terms of ability and motivation – we’re going to get the best by being available to the widest group possible."

To see the result for yourself, visit the Contagious Maths page here on Plus, or if you're a school teacher or student, the corresponding page on NRICH. Enjoy!

Play Lucky Dip!

The Lucky Dip interactivity was created by our friend, Oscar Gillespie from NRICH.

The interactivity works like our game of Lucky Dip. Each person in a population is represented by a capsule which is drawn at random. By default the reproduction ratio R (the number of people an infected person goes on to infect on average) is set to 2.

Begin by clicking 'Run one generation'. You can watch the jumbler working, or click "Next" to skip the animation.

The jumbler will release a single capsule with a red token, which represents a single infected person. The screen will now indicate that there will be '2 infected' in the next generation.

When you click 'Next', you will have a choice:

  • Click 'Run one generation' again, to see what happens in the next generation
  • Click 'Run to the end', to see a chart showing the number of infections in each generation

Click the purple cog in the interactivity to get to the "Settings" menu where you can change the population size, the value of R, and how many statistics you want to see about your growing epidemic. After changing any of these, click one of the two buttons at the bottom of the "Settings" page (either "In the current window" or "In a resizeable pop up window") to return to the interactivity where you can run your epidemic with the updated settings.

To see this interactivity in context, visit the Contagious Maths page!