The R number, the classic measure of how easily an infectious disease spreads, is how New Zealand crushed community transmission. But it’s also a clever guide to a much bigger picture, writes Jenny Nicholls.

Predicting how the global Covid-19 pandemic will progress can seem impossible, with graphs of cases from other countries beginning to look like blueprints for a rollercoaster. Where will it all end? Our best estimates come from epidemiologists, who use maligned techniques like “modelling” and “R” to help figure out what will happen next. 

Today most of us are reluctantly getting to grips with the “reproduction number” R – the classic measure of how easily an infectious disease spreads. All over the world, governments are beginning to use it as a sensor for trouble, like a sea of frowning Hollywood submarine captains tapping their gauges. 

The Rules of Contagion is a new book by 33-year-old London academic (and Twitter star – @AdamJKucharski) Adam Kucharski, an associate professor at the London School of Hygiene & Tropical Medicine. Kucharski is interested in the mathematical analysis of infectious disease outbreaks but despite this, it’s easy to like his book. He doesn’t rely on graphs and equations to explain R and herd immunity, but sympathetic tales of the men and women who figured all this stuff out.

If R is higher than one, an infected person can be expected to share their microbial guest with one or more others, and infections will tend to outpace recoveries. If R is below one, hurrah! Everyone can breathe more easily.

R, in other words, is elastic, an estimate depending on four factors that are tricky to measure: the length of time a person is infectious; the average number of people they interact with each day; the probability their contact will become infected; and the susceptibility of a population. 

Social inequality and living conditions affect some of these factors. Without cure, effective treatment or vaccine, really only one of these can be changed relatively easily in a privileged society. During the level four lockdown, our average daily contacts (number two in the list) dropped so dramatically that our Covid-19 “effective” R value dwindled to 0.35 – an astonishingly low figure. (This was estimated by the team from Te Pūnaha Matatini: the Centre for Complex Systems and Networks, hosted by the University of Auckland).

0.35! This R value is how we crushed community transmission – for now, at least.

Outside New Zealand, R values ranging from 1.5 to 6 have been reported for Covid-19, according to the same group, although others put it at 2.5. 

To help get your bearings, smallpox (now extinct “in the wild”) had an R of 4-6 (with a risk of death of about 30%, unless you were a baby, in which case it was higher). 

Chickenpox is even more infectious, with an R of 6-8. The R heavyweight is measles, one of the most infectious diseases on the planet. In an unvaccinated and susceptible community, one case can lead to 20 or more, on average. The New York Times records R values for measles ranging from 3.7 to 203.

Welcome to the world of mathematical modelling. 

It might sound messy, says Kucharski, but, “in essence, a model is just a simplification of the world, designed to help us understand what might happen in a given situation. Mechanistic models are particularly useful for questions that we can’t answer with experiments. If a health agency wants to know how effective their disease control strategy was, they can’t go back and rerun the same epidemic without it.” 

Although this book was written before the pandemic, it is a clever guide to a bigger picture – a much bigger picture. These “rules of contagion” can be applied to financial panics, epidemics of gang violence, the spread of ideas, or online misinformation. Anything, in fact, that can “go viral”.

Unlike the armchair scientists we meet online, in Kucharski’s world uncertainty isn’t a weakness – it’s a tool of the trade. “In outbreak analysis, the most significant moments aren’t the ones where we’re right,” he says. “It’s those moments when we realise we’ve been wrong. When something doesn’t look quite right: a pattern catches our eye, an exception breaks what we thought was the rule.” These are the moments, he says, “that allow us to unravel chains of transmission, searching for weak links, missing links and unusual links”.

Auckland University professor Shaun Hendy led the Te Pūnaha Matatini team that modelled scenarios for Covid-19 in New Zealand. “Kucharski has been one of the key international scientists in the Covid-19 response, putting his deep expertise to work, as well as communicating his work as he goes,” Hendy says. “He is well worth a follow on Twitter, if you want an informed cutting-edge perspective on the science of Covid-19.”

Give models a chance

It is easy to attack the projections made by a scientific model. Even renowned scientists like the epidemiologist Neil Ferguson from Imperial College, London, are accused of making “predictions” that don’t stack up. But models are often designed to show a range of scenarios. To understand the value of any model, it’s important to know the assumptions on which it was built. If you can, check the original paper before assuming the epidemiologist is a feckless dunderhead. You may well come away with a new respect for their methods and care, if not for their conclusion.

Bear in mind that a disputed number might be a projection of case numbers under a “no lockdown” scenario that never happened. If the model was an early one, it would have been built with the meagre data available in the first months of the pandemic. Countries collect data in different ways, even within their own borders. For instance, some US states count only “confirmed” Covid deaths, but not “probable” ones, making data collection across the country inconsistent. Epidemiologists, notes Kucharski, seldom have the luxury of a perfect dataset.

The increase in Covid-19 cases is exponential, so even a slight difference in assumptions can have a big effect on the end result. One way to experience this for yourself is to try Te Pūnaha Matatini’s Covid-19 Take Control, a simulator that anyone can use. The US website FiveThirtyEight has assembled 16 models published by scientists to illustrate possible trajectories of the pandemic’s US death toll. These show the assumptions underlying each model and how they lead to different estimates. The same website has a brilliant explainer on “why it’s so freaking hard to make a good Covid-19 model”.