New resources developed at Cambridge are helping students learn how maths can help tackle infectious diseases.

From measles and flu to SARS and COVID, mathematicians help us understand and predict the epidemics that can spread through our communities, and to help us look at strategies that we may be able to use to contain them.

The project, called Contagious Maths, was led by Professor Julia Gog from Cambridge’s Department of Applied Mathematics and Theoretical Physics (DAMTP), and was supported by a Rosalind Franklin Award from the Royal Society.

The curriculum-linked resources will give students between the ages 11 and 14 the opportunity to join researchers on the mathematical frontline to learn more about infectious disease spread, along with interactive tools to try mathematical modelling for themselves. Teachers receive full lesson plans, backed up by Cambridge research.

“I’ve always loved maths. I was lucky enough to have amazing teachers at sixth form who challenged me and were 100% behind me pursuing maths at the highest level, but maths as it’s taught in school can be highly abstract, so students often wonder what the point of maths even is,” said Gog, who is also Director of the Millennium Maths Project. “This is something I’m trying to help with now: to offer a glimpse from school to the research world to see the role mathematics can play in tackling important real-world problems.”

The Contagious Maths project introduces mathematical modelling; explores how mathematicians can model the spread of disease through a population and the type of questions we might think about when looking at models; and gives an insight into what mathematics researchers working on these real-life problems actually do.

“I’ve been engaged in outreach for many years at Cambridge, and the Contagious Maths project grew out of discussions with colleagues who have expertise in reaching school-age children,” said Gog. “The 11-14 age group we are targeting is a real crunch point for retaining girls in maths, and future female mathematicians. 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 of them 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 that than, and therefore so much more interesting!”

Gog hopes the Contagious Maths resources might be able to help, as they are designed to be used in regular school lessons and cover a topic with clear real-world importance.

“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,” she said. “I suspect some students will find this frustrating, and just want maths to be algorithmic exercises. But some will be intrigued, and they are the ones we are trying to reach and expose to this larger world of applied maths research.”

Contagious Maths also provides teachers with all the ideas and tools they need, so they have at their fingertips all they need to deliver these lessons, even if they have no experience with 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,” said Gog. “It’s been really fun developing these resources, teaming up with both NRICH and Plus to make the most of our combined expertise.”

In addition to the school resources, Gog and her colleagues have designed another version of Contagious Maths for a more general self-guided audience, which will work for students older than 14 or anyone, of any age, who is interested in learning about mathematical modelling.

“The paradox between the cleanness and precision of mathematics, and the utter hot mess of anything that involves biological dynamics across populations – like an outbreak of an infectious disease, is what intrigued me to stay in mathematics beyond my degree, and to move into research in mathematical biology,” said Gog.

“Elegant theoretical ideas can tell us something valuable and universal about mitigating the devastating effects of disease on human and animal populations. Super abstract equations can hold fundamental truths about real-world problems – I don’t think I will ever tire of thinking about that.”

Adapted from a Royal Society interview with Professor Julia Gog.