These Zika studies are just a few illustrations of how Ross’s methods have influenced our understanding of infectious diseases. From predicting the shape of an outbreak to evaluating control measures, mechanistic models have become a fundamental part of how we study contagion today. Researchers are using models to help health agencies respond to a whole host of outbreaks, from malaria and Zika to hiv and Ebola, in locations ranging from remote islands to conflict zones.
Ross would no doubt be glad to see how influential his ideas have been. Despite winning a Nobel Prize for his discovery that mosquitoes transmit malaria, he did not view this as his biggest achievement. ‘In my own opinion my principal work has been to establish the general laws of epidemics,’ he once wrote.[48] And he didn’t just mean disease epidemics.
Although kermack and mckendrick would later extend Ross’s mosquito theorem to other types of infections, Ross had wider ambitions. ‘As infection is only one of many kinds of events which may happen to such organisms, we shall deal with “happenings” in general,’ he wrote in the second edition of The Prevention of Malaria. Ross proposed a ‘Theory of Happenings’ to describe how the number of people affected by something – whether a disease or another event – might change over time.
Ross suggested that there are two main types of happening. The first type affects people independently: if it happens to you, it generally won’t increase or decrease the chances of it happening to someone else afterwards. According to Ross, this could include things like non-infectious diseases, accidents or divorce.[49] For example, suppose there is a new condition that can randomly affect anyone, but at first nobody in the population has it. If each person has a certain chance of becoming affected every year – and remains affected from that point onwards – we’d expect to see a rising pattern over time.
Growth of an independent happening over time. Example shows what would happen if everyone had a 5 per cent or 10 per cent chance of being affected per year
The curve gradually flattens off, though, because the size of the unaffected group shrinks over time. Each year, a proportion of people who were previously unaffected get the condition, but because there are fewer and fewer of such people over time, the overall total doesn’t grow so much later on. If the chance of being affected each year is lower, the curve will grow more slowly initially, but still eventually plateau. In reality, the curve won’t necessarily level off at 100 per cent: the final amount of people affected will depend on who is initially ‘susceptible’ to the happening.
As an illustration, consider home ownership in the UK. Of people who were born in 1960, very few were homeowners by the age of twenty, but the majority had owned a house by the time they were thirty years old. In contrast, people who were born in 1980 or 1990 had a much lower chance of becoming a homeowner during each year of their twenties. If we plot the proportion of people who become homeowners over time, we can see how quickly ownership grows in different age groups.
Percentage of people who were homeowners by a given age, based on year of birth
Data: Council of Mortgage Lenders[50]
Of course, home ownership isn’t completely random – factors such as inheritance influence people’s chance of buying – but the overall pattern lines up with Ross’s concept of an independent happening. On average, one twenty-year-old becoming a homeowner won’t have much effect on whether another gets on the housing ladder. As long as events occur independently of one another at a fairly consistent rate, this overall pattern won’t vary much. Whether we plot the amount of people who are on the housing ladder by a certain age, or the chance your bus has arrived after a certain time waiting, we’ll get a similar picture.
Independent happenings are a natural starting point, but things get more interesting when events are contagious. Ross called these types of events ‘dependent happenings’, because what happens to one person depends on how many others are currently affected. The simplest type of outbreak is one where affected people pass the condition on to others, and once affected, people remain so. In this situation, the happening will gradually permeate through the population. Ross noted that such epidemics would follow the shape of a ‘long-drawn-out letter S’. The number of people affected grows exponentially at first, with the number of new cases rising faster and faster over time. Eventually, this growth slows down and levels off.
Illustrative example of the S-shaped growth of a dependent happening, based on Ross’s model. The plot shows the growth of a more contagious and less contagious happening
The assumption that people remain affected indefinitely doesn’t usually apply to infectious diseases, because people may recover, receive treatment, or die from the infection. But it can capture other kinds of spread. The S-shaped curve would later become popular in sociology, after Everett Rogers featured it in his 1962 book Diffusion of Innovations.[51] He noted that the initial adoption of new ideas and products generally followed this shape. In the mid twentieth century, the diffusion of products, like radios and refrigerators, all traced out an S-curve; later on, televisions, microwave ovens and mobile phones would do so as well.
According to Rogers, four different types of people are responsible for the growth of a product: initial uptake comes from ‘innovators’, followed by ‘early adopters’, then the majority of the population, and finally ‘laggards’. His research into innovations mostly followed this descriptive approach, starting with the S-curve and trying to find possible explanations.
Ross had worked in the opposite direction. He’d used his mechanistic reasoning to derive the curve from scratch, showing
