Covid-19 response team: Modellers help conquer that steep cases curve

Astrophysicist uses his mathmatical models to model numbers and trends from virus

Prof Turlough Downes usually applies his mathematical modelling skills to distant star systems, but he is now helping disease experts to model the course of the Covid-19 pandemic.

As an astrophysicist based at DCU School of Mathematical Sciences, he researches star systems in far-flung regions of our galaxy. He is the first to admit he knows little about epidemics but he has experience of working with challenging data.

“Like many people, when this virus started to spread around the world, I was alarmed and I wanted to do something,” says Downes. “I know nothing about epidemiology, but I work on the formation of black holes and planets around distant stars, so I do know about building mathematical models from sparse data with gaps in and lots of noise in it. I started to think about how to model the numbers and trends from the virus.”

Downes contacted infectious disease expert Prof Sam McConkey at the Royal College of Surgeons in Ireland, and they set up a collaboration to try to improve mathematical models of Covid-19 spread.

Mathematical models use numbers, equations and rules to describe the likelihood of how many people the Sars-CoV-2 virus is likely to infect over the coming days and weeks, but there are several challenges involved, he notes.

“There are many gaps and variations in the information. This virus is spreading very rapidly, and not necessarily consistently from person to person, and the data we have do not include all infections – so you have to look at the models and their predictions as a guide.”

Working with McConkey and Prof Noel McCarthy from the University of Warwick and Dr Sean Delaney, Downes has been exploring how to refine mathematical forecasts of the viral spread, factoring fast-changing elements into the equations.

“When there is a change, like the schools closing or where we narrow the criteria for testing people, we have to take that into account,” he adds.

Predicted projections

He finds some comfort that numbers predicted by the mathematical models he works on are similar to the official projections produced by the disease experts. But he finds little comfort in the nature of the growth curve.

Getting away from the exponential growth curve was critical. “The growth curve that we want to flatten, the one that heads up very quickly on the graph, that is an exponential function,” he explains.

“And when you have an exponential function, the numbers of cases rise extremely rapidly. No healthcare system can cope with the rate of increase of cases on an exponential function. That is why we want to flatten the curve. If you have got exponential growth, you are in trouble very quickly.”

Physical distancing is a small act, but if we do it consistently over time, that adds up to a powerful way to slow the spread of the virus and pull back from the exponential growth – as has now been achieved, Downes says. However, there is no room for complacency, he adds. “Exponential growth is relentless, even if you have small numbers of cases, if we are on exponential growth the numbers can still grow extremely rapidly.”

Downes hopes the official figures will consistently overestimate the actual numbers of cases that arise. “That is the pattern you want to see,” he says. “If we have projections based on exponential growth, but then the actual numbers are lower, it means the virus is slowing and the health system has more of a chance to treat patients who are severely ill.”

He also hopes to be able to turn his attention back to outer space soon. “I had expected that in this time of working from home I would be modelling data from a molecular cloud near a star system about 7,500 light years away, but then I started on this work,” he says.

“And I am only able to use these skills on the pandemic data because I have been developing them doing fundamental research in a university over the past two decades. It’s important to remember that universities are not only for education; they are also repositories of knowledge and skills that can be called upon in times of need.”