I had promised to write about models that I think succeed on a very high level and so let me start that series of posts by discussing Ronald Ross’ so-called mosquito theorem.
If you go running in Kingston, Ontario, along the west bank of the start of the Rideau Canal, past the dock and towards the Kingston-Whig Standard headquarters, you will come across a Celtic cross that reads:
In memory of an estimated one thousand Irish labourers and their coworkers who died of malaria and by accidents in terrible working conditions while building the Rideau Canal, 1826-1832.
I didn’t think too much of that at the time, but later I was trying to recall the disease that was mentioned. Malaria? In Kingston? In Canada? Could that be right?
Ronald Ross. This picture was taken from Wikipedia and is in the public domain.
And so I read up on the details (see for example here and here) and, sure enough, malaria had been endemic in North America and was eradicated through the use of insecticides and mosquito control.
Ronald Ross identified the anophelene mosquitoes as the vector for malaria transmission and developed a mathematical model that showed that malaria could be eradicated as long as the number of mosquitoes per human was brought below a threshold value, which was significant because malaria could then be eliminated without needing to kill every mosquito. Given that introduction, it’s not hard to see why I might consider this a great mathematical model: (1) malaria was eradicated in North America – an extremely impressive achievement, and (2) the ‘mosquito theorem’ turned out to be correct.
Ross sounds like an amazing guy and I’m not sure if there is a lesson here or if it’s just that he was flat out brilliant. Having said that, I think one of the reasons Ross’ work was so successful was because mathematical modelling was just one facet of his arsenal – he likely derived the model because he needed the result to help design and lobby for prevention strategies. If there is any lesson here for today’s theoretician it might be that Ross’ success underscores the importance of collaboration with empiricists, ecologists, clinicians and other experts.
In 1902, Ross was awarded the Nobel Prize in medicine and physiology, however, this was after Ross’ experimental work on malaria transmission and before Ross derived his first epidemiological model in 1908. Yet, despite Ross having made numerous and varied contributions, the Nobel Laureates webpage singles out mathematical modelling as Ross’ greatest contribution:
He made many contributions to the epidemiology of malaria and to methods of its survey and assessment, but perhaps his greatest was the development of mathematical models for the study of its epidemiology, initiated in his report on Mauritius in 1908, elaborated in his Prevention of Malaria in 1911 and further elaborated in a more generalized form in scientific papers published by the Royal Society in 1915 and 1916. These papers represented a profound mathematical interest which was not confined to epidemiology, but led him to make material contributions to both pure and applied mathematics.
Just Simple Enough: The Art of Mathematical Modelling 
A great post Amy! There is a short biography of the remarkable Ronald Ross (along with Robert Koch and Giovanni Grassi) in “The Malaria Capers” by Robert Desowitz. The book does not cast Ross as flat out brilliant in every respect (“the man most unlikely to succeed. Ignorant of zoology, he hardly knew one end of a mosquito from the other, let alone one mosquito species from another”) and it implies that he never quite appreciated the fact that anophelene (“dapple-winged”) mosquitoes were the sole vectors of human malaria (Ross used avian malaria as his primary model). Nevertheless Ross was clearly a driven man and a supremely talented polymath (he was also a poet and playwright). For another polymath with an even earlier mathematical model (this one evolutionary) you might look at Johannes (Fritz) Muller – however the implications of his model (for a form of mimicry that now carries his name) have far less reach!
I did not know about the criticism of his lack of zoological thoroughness; thanks for bringing that up. Thanks for the Muller suggestion too.