Pandemic by numbers:  mathematical equations help keep us safe

James McCaw is Professor of Mathematical Biology at the University of Melbourne. His 2024 ARC Laureate Fellowship will focus on preparations for the next pandemic.

Mathematical biology is a very broad field. My group works on infectious diseases, studying how viruses and parasites spread within our body, and how they transmit from person to person. We use mathematical models to try and simulate those processes. And we use a lot of statistical analysis to understand data that is measuring those processes. We then bring our biological knowledge and mathematical analysis together to try and say new things about the biological world itself. We then work in spaces like epidemiology and public health to help support responses to events like COVID 19.

It was on 16 January 2020 that the World Health Organisation first convened a teleconference for people like me, with expertise in pandemic response, on what was developing in Wuhan, China. It was clear that a new virus was infecting humans, but it wasn’t yet clear how it was spreading.

James mccaw (supplied)
James McCaw (supplied)

It took another three days or so before we as a global community were almost certain that it was spreading directly from human to human, and that we were facing a global pandemic. But we didn’t know how severe it would be.

I was sitting on the emergency response committee at the Commonwealth level, meeting at least once, if not twice a day. For those first few weeks we had very little data. But because of some amazing empirical work, we knew it was a coronavirus: a respiratory virus. We already knew how flu spread, and how the original SARS spread, and because we had those statistics and data, we were able to form a mathematical understanding of what we were potentially facing.

When I say a mathematical understanding, I mean a conceptual, theoretical model of how things behave. Just as Newton’s laws and Einstein’s laws are a mathematical model, we have mathematical models of disease transmission.

This is an important point. I believe science progresses most rapidly and effectively when it has a balance between empirical observation and theoretical considerations – when you think deeply about the processes that are occurring and how they would lead to the data that you see. This balance between theory and experiment has been embraced for centuries in Physics, and it serves that science well. And it’s starting to happen more and more in fields of biology, which is very exciting. Like helping society find a way through these pandemics.

With these models, we can reason on what might happen. Where we know that we don’t know things, we capture the uncertainty in our models. And that’s what we were doing in early February 2020. We were able to say that if this virus spreads very much like flu, it might have these characteristics. But if it spreads more like original SARS, it would have these characteristics, and spread this quickly. We were also able to predict from some very early characteristics that it looked a little bit like both. And as it turns out, that’s where it was, in between the two of them.

In this way we were able to make useful predictions about what this new pathogen might do when it got into Australia and began to spread in the population. And it was mathematics that was giving us a qualitative insight, though not a quantitative one. This is another important point: most of the work from mathematics provides you with qualitative understandings of things. It’s only when you then bring the mathematics and the data together that you get a quantitative understanding.

When someone says maths is about the numbers, that’s actually rarely the case. It’s really maths combined with the data – the statistics – that’s all about the numbers. The maths is about logical, reasoned thought and understanding the processes that drive transmission.

Most of the mathematics we use is calculus. It’s very similar to the maths that you’re just starting to learn in year 11, and certainly know quite a lot of in year 12. Calculus isn’t a familiar word to many people, but it’s essentially a study of the rate of change through time.

First, we ask questions and write down equations. For example, the number of people who will become infected tomorrow is related to how many people are currently infected, and how many people are susceptible in the population. If you reason on those sort of logical thought experiments, you can write down equations which very accurately capture what happens when you observe epidemics, and these equations allow you to make accurate predictions about what is likely to happen and how different interventions can change what happens. The models explain why you get epidemic waves, why you get the early exponential growth, then the peaks, the declines, and then the next wave. 

My colleagues and I worked very hard to communicate issues of scientific knowledge and scientific uncertainty, then put that into the government decision-making processes: it was then up to our elected representatives and people in the public service to make decisions. They did their job, and we did our job, and Australians did their job by following the advice. But we were aware that there were going to be members of the community who would disagree, and some of these people would express their views in very unpleasant ways. It wasn’t easy at times, and I didn’t see the worst of it, but many of my colleagues did.

COVID19 is a nasty pathogen that will continue to impact us negatively for decades to come. For the first few years of the pandemic, we had little immunity, rampant spread at a global scale, and there were severe clinical outcomes. But today most people in the population have been vaccinated and/or infected a few times. We are in a process of bringing COVID19 into the suite of all the different pathogens and health issues that we manage on a day-to-day basis, and that’s necessary because it’s going to be with us forever.

We need to manage it efficiently and effectively. Importantly, the solution isn’t to say that the flu is fine, so COVID is fine. It’s actually to recognise that we can do better against both viruses, reducing the burden of flu and COVID on the community.

Through my ARC fellowship, I’m aiming to train the next generation of mathematicians and data scientists to support government and the community to better understand, and reduce the impact of, infectious diseases.

As told to Graem Sims

Also in this series on 2024 ARC Laureate Fellows:

Energy transition and communities: Professor Chris Gibson

Plate tectonics: Professor Alan Collins

Predicting groundwater discharge Professor Andrew Baker

Unravelling the mysteries of the immune system Professor Gabrielle Belz

Researchers hope to monitor Antarctic vegetation remotely Professor Sharon Robinson

How to build a quantum computer Professor Andrea Morello

More about maths and pandemics

Buy cosmos print magazine

Please login to favourite this article.