Since the COVID-19 pandemic began, it would be fair to say that many of us have become obsessed with numbers.
The number of cases of coronavirus, the number of deaths and so on.
Mathematician Associate Professor Alex James is no different – but for her there are some numbers that are more important than others.
Photo: AFP
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Mathematician Associate Professor Alex James, from the University of Canterbury. Photo: UCNZ
Alex James is a mathematician at the University of Canterbury and an investigator with Te Pūnaha Matatini, New Zealand's Centre of Research Excellence for Complex Systems and Data Analytics.
She is interested in creating mathematical models for what are known as complex systems, including ecology and infectious diseases.
When it came to the coronavirus pandemic, Alex and colleagues at Te Pūnaha Matatini decided to use their collective expertise to model the situation in New Zealand as it developed. They have produced a number of models, which they are providing to health officials to help with decision-making.
These models complement others being worked on by groups such as Michael Baker and Nick Wilson at the University of Otago, amongst others.
The mathematical modelling of a disease such as coronavirus is not about precise predictions.
“We’re not always trying to predict exact numbers,” says Alex. “We’re often thinking ‘in two weeks‘ time is it going to be going up? Is it still going to be going up? Is it going to be going down?’ It’s more general questions like that rather than what will the number exactly be.”
Alex says that she thinks mathematical modelling is both an art and a science.
“The art is to think this is complicated, there are a million different things going on here – but what are the most important ones? Can I boil this down to just two or three ideas and capture a lot of that complexity in just a small number of features.”
One magic number
“In epidemiological models, [such as] models of disease spread, we have one magic number,” says Alex. “We call it R0 or R nought.” It is also known as R zero, the reproduction number or reproductive ratio.
“R nought is ‘if I have an infection, how many people am I likely to infect’?”
An R0 of two means that on average one person will spread the infection to two others. Anything above one means the number of cases will begin to increase exponentially. An R0 of less than one means the infection will eventually die out.
R nought is a useful number at the beginning of an epidemic when there is zero immunity in the population.
Alex says that when it comes to COVID-19, her team’s first question was “if this all goes horribly wrong, what would be the outcome of that?”
They modelled this using an SIR model. The name refers to Susceptible, Infected, Removed, and the terms refer to individual susceptibility to the infection, the rate at which infections actually occur, and the rate of at which infections are removed from the population as people either recover or die.
The Te Pūnaha Matatini team used data from overseas to show how effective different policies might be in controlling the spread of infection. Alex says that “with all the social distancing policies that so many countries are putting in place, we can see that on the whole those policies are bringing R noughts of less than one.”
On the eve of New Zealand’s level 4 lockdown, Alex and Te Pūnaha Matatini colleagues released this first modelling, in a paper called ‘Suppression and mitigation strategies for control of COVID-19 in New Zealand.’ The paper showed that with early and strict intervention, it should be possible to suppress or put a lid on the infection rate here.
New models
Since that initial SIR model, Alex and her colleagues have been working on other kinds of mathematical models. They’re using global data about coronavirus infections and death rates as they come to hand each day. These numbers giving us a clearer picture of how the virus actually works, and how many people it’s infecting and killing.
The next Te Pūnaha Matatini paper, titled ‘A stochastic model for COVID-19 spread and the effects of Alert Level 4 in Aotearoa New Zealand,” came out late last week. It used a different kind of mathematical model and found that existing controls had already begun to have an effect by the end of March and that we might even be able to eliminate the disease, but only by continuing the lockdown beyond the initial 4 weeks.
COVID-19 modelling prediction from Te Pūnaha Matatini:the Centre for Complex Systems and Networks. The paper "Stochastic model for COVID-19 spread and the effects of Alert Level 4 in Aotearoa New Zealand" was first made available on 9 April 2020. Photo: Te Pūnaha Matatini
On Thursday 16 April 2020, Professor Sean Hendy from Te Pūnaha Matatini told RNZ that the team’s latest modelling on the risks of an outbreak from easing the lockdown is due out shortly. He told Te Hiku Media on Friday 17 April that after three weeks the lockdown had achieved an R nought of 0.5.
20 April: here is a link to the latest modelling: Estimated inequalities in COVID-19 infection fatality rates for Atearoa New Zealand.
'All models are wrong, but some are useful'
Alex agrees with a well-known comment by statistician George Box that ‘all models are wrong, but some models are useful.’
“He was absolutely right,” says Alex. “Yes, all models are wrong, but we hope that we can come up with models that are useful.”
“If you wanted me to predict how many cases there will be tomorrow, no I can’t do that. But once I’ve seen how many cases there are then I can start to think about the long-term trend. Is it going up, is it going down and how fast is it going down.”
To find out more about mathematical models being used to understand how the coronavirus pandemic might play out in New Zealand, listen to the full interview with Alex James.
Our Changing World has been providing scientific context to the COVID-19 pandemic:
Virus 101 - the science of viruses.
Our immune system vs coronavirus – ‘I think of it as an orchestra’
