ROLE MODELS IN A TIME OF PENDEMIC
THE FIRST VIDEOCONFERENCE – like the many that followed – was late at night. From his home in suburban Melbourne, James McCaw joined fellow disease trackers from around the world in mid-January to discuss some of the early data emerging from Wuhan, the Chinese city at the epicentre of what became the COVID-19 global pandemic.
The news wasn’t good. The new virus was leaving dozens sick; a handful had already died. More worrying still, epidemiologists at Imperial College London estimated the transport and industrial hub in central China harboured many more cases of infection than had been reported. “It was clearly spreading,” says McCaw, who uses mathematical models to trace how diseases do just that, “but we didn’t really know what the consequences of it would be.”
Since January it has been McCaw’s job, along with his long-time collaborator Jodie McVernon and a small army of colleagues, to build mathematical projections of how an outbreak might play out in Australia, and relay that information to government officials.
While other scientists are in the midst of a Herculean effort to discover what they can about SARS-CoV-2 (see page 28), the virus responsible for COVID-19, the work of disease modellers like McCaw and McVernon – both based at the University of Melbourne’s Peter Doherty Institute for Infection and Immunity – has been playing an outsized role in upending life as we knew it pre-pandemic.
In Australia, as elsewhere, governments are making decisions not because they are written into a pandemic playbook, but because mathematical models – written on the fly, as the disaster unfolds – light the way.
“There is not a single pandemic plan globally that talks about lockdown as a control measure,” McVernon announced during a press conference in early April. And yet, living in some form of lockdown is exactly where vast swathes of the world’s populace found itself.
Decisions to lock the borders to foreigners, cancel sporting events and concerts, shutter schools and tell people to stay in their homes have been taken, in large part, because of the mathematical models that McCaw, McVernon and their colleagues have built. They determine when restrictions begin, and when they end. So, how did this one line of evidence become so influential?
THE FOUNDATIONS OF MODERN epidemic modelling were laid in the early 20th century. In 1897, the British army surgeon Ronald Ross demonstrated that the malaria parasite is transmitted by mosquitoes, not through contaminated water as others had assumed. After retiring from the army – and winning the Nobel Prize for his discovery in
1902 – Ross spent much of the first decade of the new century travelling around Africa and the Mediterranean drumming up support for a fight against the mosquito. Not everyone bought the idea that reducing mosquito numbers could eradicate malaria, but maths, he decided, could provide the evidence.
Others before him had attempted to describe how diseases spread using mathematical principles, but Ross pushed to establish mathematical epidemiology – what he called “a priori pathometry” – as a new field of study. “All epidemiology, concerned as it is with the variation of disease from time to time or from place to place, must be considered mathematically, however many variables are implicated, if it is to be considered scientifically at all,” he said.
In the 1920s, two Scots took things further. Anderson McKendrick – an ex-army physician who had accompanied Ross on a malaria-fighting mission to Sierra Leone two decades earlier – teamed up with William Kermack, a young biochemist who had been blinded in a lab accident.
The duo devised a model that looks deceptively simple, yet forms the basis for transmission models to this day. It places people in a population into one of three buckets, marked S, I and R. Individuals are either susceptible to an infection (S), are infected (I), or have recovered or “removed” (died) (R) .
For a new virus, like SARS-CoV-2, the whole population is presumed to be susceptible at the start of the outbreak. If infection spreads unhindered, the number of susceptible people falls over time, while those who have recovered – and are presumed to be immune to reinfection and unable to pass the infection on – grow in number.
Meanwhile, the number of people infected etches out the now-familiar bell-shaped curve of sickness: a gentle incline followed by a deathly uptick, a levelling as the epidemic reaches its peak and a final downward slope as the outbreak runs out of susceptible people to infect.
The shape of the bell – whether it resembles an upturned champagne flute or a broader, less precipitous, upturned soup dish – depends on how rapidly the disease is spreading. This boils down to the basic reproduction number (R ): how many people, on average, a
0 single sick person infects. Kermack and McKendrick noticed that the curve could only keep rising as long as that number is
