Descriptive and mechanistic methods – one looking back and the other forward – should in theory converge to the same answer. Take the descriptive approach. With enough real-life data, it would be possible to estimate the effect of mosquito control: tip over a water tank, or remove mosquitoes in some other way, and we can observe what happens. Conversely, the predicted effect of mosquito control in Ross’s mathematical analysis should ideally match the real impact of such measures. If a control strategy genuinely works, both methods should tell us that it does. The difference is that with Ross’s mechanistic approach, we don’t need to knock over water tanks to estimate what effect it might have.
Mathematical models like Ross’s often have a reputation for being opaque or complicated. 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. Likewise, if we want to know what a future pandemic might look like, we can’t deliberately release a new virus and see how it spreads. Models give us the ability to examine outbreaks without interfering with reality. We can explore how things like transmission and recovery affect the spread of infection. We can introduce different control measures – from mosquito removal to vaccination – and see how effective they might be in different situations.
In the early twentieth century, this approach was exactly what Ross needed. When he announced that Anopheles mosquitoes spread malaria, many of his peers were unconvinced that mosquito control would reduce the disease. This made descriptive analysis problematic: it’s tricky to assess a control measure if it’s not being used. Thanks to his new model, however, Ross had convinced himself that long-term mosquito reduction would work. The next challenge was convincing everyone else.
From a modern viewpoint, it might seem strange that there was so much opposition to Ross’s ideas. Although the science of epidemiology was expanding, creating new ways to analyse disease patterns, the medical community didn’t view malaria in the same way that Ross did. Fundamentally, it was a clash of philosophies. Most physicians thought about malaria in terms of descriptions: when looking at outbreaks, they dealt in classifications rather than calculus. But Ross was adamant that the processes behind disease epidemics needed to be quantified. ‘Epidemiology is in fact a mathematical subject,’ he wrote in 1911, ‘and fewer absurd mistakes would be made regarding it (for example, those regarding malaria) if more attention were given to the mathematical study of it.’[28]
It would take many more years for mosquito control to be widely adopted. Ross would not live to see the most dramatic reductions in malaria cases: the disease remained in England until the 1950s, and was only eliminated from continental Europe in 1975.[29] Although his ideas eventually started to catch on, he lamented the delay. ‘The world requires at least ten years to understand a new idea,’ he once wrote, ‘however important or simple it may be.’
It wasn’t just Ross’s practical efforts that would spread over time. One of the team on that 1901 expedition to Sierra Leone had been Anderson McKendrick, a newly qualified doctor from Glasgow. McKendrick had top-scored in the Indian Medical Service exams and was scheduled to start his new job in India after the Sierra Leone trip.[30] On the ship back to Britain, McKendrick and Ross talked at length about the mathematics of disease. The pair continued to exchange ideas over the following years. Eventually, McKendrick would pick up enough maths to try and build on Ross’s analysis. ‘I have read your work in your capital book,’ he told Ross in August 1911. ‘I am trying to reach the same conclusions from differential equations, but it is a very elusive business, and I am having to extend mathematics in new directions. I doubt whether I shall be able to get what I want, but “a man’s reach must exceed his grasp”.’[31]
McKendrick would develop a scathing view of statisticians like Karl Pearson, who relied heavily on descriptive analysis rather than adopting Ross’s mechanistic methods. ‘The Pearsonians have as usual made a frightful hash of the whole business,’ he told Ross after reading a flawed analysis of malaria infections. ‘I have no sympathy with them, or their methods.’[32] Traditional descriptive approaches were an important part of medicine – and still are – but they have limitations when it comes to understanding the process of transmission. McKendrick believed the future of outbreak analysis lay with a more dynamic way of thinking. Ross shared this view. ‘We shall end by establishing a new science,’ he once told McKendrick. ‘But first let you and me unlock the door and then anybody can go in who likes.’[33]
One summer evening in 1924, William Kermack’s experiment exploded, spraying corrosive alkali solution into his eyes. A chemist by training, Kermack had been investigating the methods commonly used to study spinal fluids. He was working alone in Edinburgh’s Royal College of Physicians Laboratory that evening, and would eventually spend two months in hospital with his injuries. The accident left the 26-year-old Kermack completely blind.[34]
During his stay in hospital, Kermack asked friends and nurses to read mathematics to him. Knowing that he could no longer see, he wanted to practise getting information another way. He had an exceptional memory and would work through mathematical problems in his head. ‘It was incredible to find how much he could do without being able to put anything down on paper,’ remarked William McCrea, one of his colleagues.
After leaving hospital, Kermack continued to work in science but shifted his focus to other
