Controlling disease is not just a question of medicine or politics; it’s also a question of maths.  Adam Kucharski explained why.

What does the phrase ‘mathematical modelling’ suggest to you? It might sound abstruse, unrelated to matters of life and death; but maths is one of our most powerful weapons in the fight against disease. How can we measure disease spread? How can a few key people shape an outbreak? Which infections are the hardest to control? In the Rosalind Franklin Award Lecture at this year’s British Science Festival, Adam Kucharski addressed these questions.

Adam is Assistant Professor at the London School of Hygiene & Tropical Medicine. He’s studied avian flu in China, monkey pox in central Africa and dengue fever in Fiji. He’s supplied vital information to the World Health Organisation and other agencies responding to the recent Ebola outbreak in west Africa. The models he builds can help us evaluate, not just how epidemics spread, but the effectiveness of the measures we take to control them.

It all starts with ‘the reproduction number’: the average number of infections one case generates during its infectious period in an otherwise uninfected population. Ebola, for example, has a reproduction number of 1-2 – much the same as flu. Measles, by contrast, enjoys a hefty reproduction number of 15-20. High reproduction numbers characterise infections, like measles, that we categorise as childhood diseases: you’re more likely to get it early in life.

We created two ‘epidemics’ in the audience, showing how the basic exponential model – one person infects two, those two infect four, and so on – differs from a more sophisticated model, in which we chose who to ‘infect’ before ourselves becoming ‘infected’: a model that resembles a real epidemic rather more closely.

Those choices in the demonstration stood for our cultural choices about the social contacts we make. And those contacts affect the spread of disease in complex ways. Italians, for example, on average, generate more social contacts than Germans. But perhaps more significant than national differences are the hotspots created by occasional social events where a small number of people can generate a large number of infections. It’s called ‘super-spreading’: think of children returning to school after the holidays, or patients crowded together in a hospital. One of the recent Ebola outbreaks originated at a funeral. Super-spreading creates patterns in which a disease will often die out quickly after one or two contacts, but may sometimes flare into a major outbreak. Target the hotspots – what Adam calls the “highly transmissible nodes” in a community – and you may be able to control an outbreak more rapidly.

Do other kinds of intervention – international aid, for example – make difference? In the case of providing beds for Ebola patients in west Africa, the answer was a definite ‘yes’; but acting more quickly, according to Adam’s models, would have saved even more lives. And vaccination? How to trial the effectiveness of a vaccine if you need time to develop one, and then introduce it just as an epidemic has ‘turned over’? You need to design the trial to fit the epidemic.

And that’s tricky, because a bewildering array of variables affects how easy or difficult a disease can be to control. Among the more obvious are the length of an infection’s incubation period, and the ease of diagnosis – both of which affect our ability to trace an infected person’s recent social contacts. International air travel adds a further level of complexity. Adam borrowed a quote to summarise the issue: “If you’ve seen one epidemic, you’ve seen – one epidemic.”

So, from trying to forecast outbreaks right through to designing trials and how you respond to them, we need to think about the dynamics of infection. In Adam’s closing words: “Controlling disease is not just a question of medicine, biology or politics; it’s also a question of mathematics.”

Alan Barker, British Science Festival Swansea, September 2016. Alan Barker is a writer and training consultant specialising in communication skills.  He is Managing Director of Kairos Training Limited.