ROLE MODELS IN A TIME OF PANDEMIC
COVID-19 has brought with it a swathe of decisions and directions about if and when we can be close to others. DYANI LEWIS investigates the outsized influence of mathematical modelling when life becomes lockdown.
Roman Hill grew up wanting to be a musician and experimented with long-form synthesiser music, bending circuits to transform instruments to play “unhearable and unbearable noises”.
“I was really playing around with textures,” he says. “Then I realised that people understood weird textures in an image really fast, that they could really capture its beauty.” A friend suggested the milk experiment*; Hill tried it, and was hooked. He travelled to the US for six months to immerse himself in chemistry and fluid dynamics, and has since produced a number of short films culminating in As above.
Hill experiments with a wide variety of fluids, all readily available. For his next film he says: “I’m using hot water, some flowers I found in the garden. Filming them really close will make it look like it’s another world.”
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 single sick person infects. Kermack and Mckendrick noticed that the curve could only keep rising as long as that number is greater than one. The turning point at the apex of the bell marks the point where the reproduction number dips below one – each person infects fewer than one other and the outbreak starts to fizzle.
To prove they were on the right track, Kermack and Mckendrick overlaid their theoretical curve onto data from a real-world epidemic: an outbreak of plague that struck the Indian city of Bombay (now Mumbai) in 1905 and 1906. The deaths recorded each week lined up with their bell.
“The mathematics of it is not complicated,” says Raina Macintyre, head of the Biosecurity Program at the Kirby Institute at the University of NSW. “What’s complicated is the parameters and the assumptions that go into the model.”
The simplest SIR models assume everyone in the population has an equal risk of being infected and is equally infectious once sick. That’s not true of influenza: young children long on sniffles and short on personal boundaries are the primary spreaders of the flu. And it doesn’t appear to be true of SARS-COV-2 either: children appear less likely than adults to catch or pass on the virus.
Models today are more sophisticated. They divide the population into smaller tubs – based on age and health status, say – that try to account for different people’s risk of being infected and their differing propensity to infect others. The stages of disease are also more finely compartmentalised to reflect how likely the infection is to jump from one person to the next at different stages, from the point of exposure through to full recovery or death.
IN 2003, THE WORLD HEALTH ORGANISATION issued a resolution urging its member states to plan for the next flu pandemic: up vaccination rates, strengthen surveillance to spot outbreaks early, and stockpile antivirals and other essential medicines. The 2008 Australian Health Management Plan for Pandemic Influenza helped us navigate the 2009 swine flu pandemic, which killed 191 people across the nation.
Mccaw and Mcvernon have been working with the Australian government to prepare for the next influenza pandemic for the past decade and a half. It was COVID-19 that arrived, but the planning wasn’t in vain. “Flu and the coronaviruses differ in fundamentally important ways biologically,” says Mccaw, but “the way that we break down the problem, unpick it, think through the possible response options, is very similar… That’s incredibly valuable.”
Through January, as the COVID-19 situation worsened, Mccaw and his team used mathematical modelling to see whether the Australian healthcare system was up to the task that lay ahead. What was the likely shape of the epidemic curve in Australia if
left unchecked, or if hit with disease-stopping interventions? Some of the assumptions they used were harvested from crucial – yet still uncertain – pieces of information coming out of China. Using data from the early days of an epidemic is fraught. Early reports can miss mild and asymptomatic cases, and details of when each person first detects a sore throat or sniffly nose can be unreliable.
Nevertheless, it looked like the outbreak was doubling every 6.4 days, and case records suggested an incubation period (how long it takes for symptoms to show up after infection) of just over five days, with people able to transmit the virus for two days before they showed symptoms. These values, in turn, pointed to an R0 of around 2.5, though estimates at the time ranged from as low as 1.5 to more than five depending on which cases were used for the calculation.
A final assumption – based, again, on case reports – approximated how many people who got sick would end up in hospital. Few children, but up to one in five people over the age of 80, would end up in the intensive care unit (ICU). “By early February, we had produced some very early plausible scenarios, which had terrifying numbers in them,” says Mccaw.
If allowed to spread uncontrolled, COVID-19 would infect 90% of the population. The healthcare system would be overwhelmed for weeks, and for every three people receiving the intensive care treatment they required, 17 others would go without. Quarantining the sick and keeping the seemingly well apart could stem transmission, reducing the onslaught.
The federal and state governments took note of this and of subsequent models Mcvernon, Mccaw and their team produced. On 1 February restrictions began, first on international travellers from China and then, in March, on travellers from elsewhere. On 24 March, returning Australians were required to self-isolate for two weeks and banned from travelling overseas. Police were given the authority to fine people not at home except for the most essential activities. Behind the scenes, hospitals diverted