Ross put the intellectual affair behind him for a while, but returned to the subject after his mosquito discovery. This time, he found a way to make his mathematical hobby useful to his professional work. There was a vital question he needed to answer: was it really possible to control malaria without removing every mosquito? To find out, he developed a simple conceptual model of malaria transmission. He started by calculating how many new human malaria infections there might be each month, on average, in a given geographic area. This meant breaking down the process of transmission into its basic components. For transmission to occur, he reasoned, there first needs to be at least one human in the area who is infectious with malaria. As an example, he picked a scenario where there was one infectious person in a village of 1,000. For the infection to pass to another human, an Anopheles mosquito would have to bite this infectious human. Ross reckoned only 1 in 4 mosquitoes would manage to bite someone. So if there were 48,000 mosquitoes in an area, he’d expect only 12,000 to bite a person. And because only 1 person in 1,000 was initially infectious, on average only 12 of those 12,000 mosquitoes would bite that one infectious person and pick up the parasite.
It takes some time for the malaria parasite to reproduce within a mosquito, so these insects would also have to survive long enough to become infectious. Ross assumed only 1 in every 3 mosquitoes would make it this far, which meant that of the 12 mosquitoes with the parasite, only 4 would eventually become infectious. Finally, these mosquitoes would need to bite another human to pass on the infection. If, again, only 1 in 4 of them successfully fed off a human, this would leave a single infectious mosquito to transmit the virus. Ross’s calculation showed that even if there were 48,000 mosquitoes in the area, on average they would generate only one new human infection.
If there were more mosquitoes, or more infected humans, by the above logic we’d expect more new infections per month. However, there is a second process that counteracts this effect: Ross estimated that around 20 per cent of humans infected with malaria would recover each month. For malaria to remain endemic in the population, these two processes – infection and recovery – would need to balance each other out. If the recoveries outpaced the rate of new infections, the level of disease eventually would decline to zero.
This was his crucial insight. It wasn’t necessary to get rid of every last mosquito to control malaria: there was a critical mosquito density, and once the mosquito population fell below this level, the disease would fade away by itself. As Ross put it, ‘malaria cannot persist in a community unless the Anophelines are so numerous that the number of new infections compensates for the number of recoveries.’
Ross calculated that even if there were 48,000 mosquitoes in a village that contained someone infected with malaria, it might only result in one additional human case
When he wrote up the analysis in his 1910 book The Prevention of Malaria, Ross acknowledged that his readers might not follow all of his calculations. Still, he believed that they would be able to appreciate the implications. ‘The reader should make a careful study of those ideas,’ he wrote, ‘and will, I think, have little difficulty in understanding them, though he may have forgotten most of his mathematics’. Keeping with the mathematical theme, he called his discovery the ‘mosquito theorem’.
The analysis showed how malaria could be controlled, but it also included a much deeper insight, which would revolutionise how we look at contagion. As Ross saw it, there were two ways to approach disease analysis. Let’s call them ‘descriptive’ and ‘mechanistic’ methods. In Ross’s era, most studies used descriptive reasoning. This involved starting with real-life data and working backwards to identify predictable patterns. Take William Farr’s analysis of a London smallpox outbreak in the late 1830s. A government statistician, Farr had noticed that the epidemic grew rapidly at first, but eventually this growth slowed until the outbreak peaked, then started to decline. This decline was almost a mirror image of the growth phase. Farr plotted a curve through case data to capture the general shape; when another outbreak started in 1840, he found it followed much the same path.[25] In his analysis, Farr didn’t account for the mechanics of disease transmission. There were no rates of infection or rates of recovery. This isn’t that surprising: at the time nobody knew that smallpox was a virus. Farr’s method therefore focused on what shape epidemics take, not why they take that shape.[26]
In contrast, Ross adopted a mechanistic approach. Rather than taking data and finding patterns that could describe the observed trends, he started by outlining the main processes that influenced transmission. Using his knowledge of malaria, he specified how people became infected, how they infected others, and how quickly they recovered. He summarised this conceptual model of transmission using mathematical equations, which he then analysed to make conclusions about likely outbreak patterns.
Because his analysis included specific assumptions about the transmission process, Ross could tweak these assumptions to see what might happen if the situation changed. What effect might mosquito reduction have? How quickly would the disease disappear if transmission declined? Ross’s approach meant he could look forward and ask ‘what if?’, rather than just searching for patterns in existing data. Although other researchers had made rough attempts at this type of analysis before,
