1.6 The Study of Epidemics

By 1915, when Ross turned his attention to the broader study of epidemics, his intent was to establish a new discipline, which he called a priori pathometry. He set out to establish the mathematical foundations for the study of epidemics [47,48]. In his 1916 paper, he wrote

It is somewhat surprising that so little mathematical work should have been done on the subject of epidemics, and, indeed, on the distribution of diseases in general.

The case for using mathematics had grown stronger as a result of a scientific revolution caused by invention of the light microscope that established a germ theory of disease, which included Laveran’s discovery in 1880. Even without knowing that bacteria, viruses, and parasites were transmitted among hosts causing disease, contagion was an impossible concept to ignore. Some mathematical work had already been done on infectious diseases, including a few models. It’s not clear whether Ross was aware of Daniel Bernouli’s mathematical model of small pox [49,50], or PD En’ko’s discrete time models for measles [51]. Ross may have known about those models, but he certainly didn’t cite them. Regardless, the mathematical study of infectious diseases in populations was, at that point in time, underdeveloped. Ross wrote:

…the principles of epidemiology on which preventive measures largely depend, such as the rate of infection, the frequency of outbreaks, and the loss of immunity, can scarceley ever be resolved by any other methods than those of analysis.

Ross proposes a rudimentary three-tiered classification system for epidemics based on the patterns of fluctuating incidence with exemplars: 1) leprosy and tuberculosis; 2) measles and malaria; 3) plague and cholera.

To what are these differences due? Why indeed should epidemics occur at all, and why should not all infectious diseases belong to the first group and not always remain at an almost flat rate?

In 1917, he teamed up with Hilda Hudson, a Cambridge mathematician, to finish the first major contribution to mathematical epidemiology, or what he called a priori pathometry [52,53]. Over 18 years (1899-1917), Ross’s ideas laid a solid foundations for the modern study of malaria transmission and theory of malaria control [2].

References

2.
Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog. 2012;8: e1002588. doi:10.1371/journal.ppat.1002588
47.
Ross R. Some a priori pathometric equations. Br Med J. 1915;i: 546–547. doi:10.1136/bmj.1.2830.546
48.
Ross R. An application of the theory of probabilities to the study of a priori pathometry. Part I. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 1916;92: 204–230.
49.
Bernoulli D, Blower S. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Rev Med Virol. 2004;14: 275–288. Available: https://www.ingentaconnect.com/content/jws/rmv/2004/00000014/00000005/art00002?crawler=true
50.
Bacaër N. Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760). A short history of mathematical population dynamics. Springer; 2011. pp. 21–30. Available: https://link.springer.com/chapter/10.1007/978-0-85729-115-8_4
51.
Dietz K. The first epidemic model: A historical note on PD En’ko. Aust J Stat. 1988;30A: 56–65. doi:10.1111/j.1467-842X.1988.tb00464.x
52.
Ross R, Hudson HP. An application of the theory of probabilities to the study of a priori pathometry. Part II. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences. 1917;93: 212–225.
53.
Ross R, Hudson H. An application of the theory of probabilities to the study of a priori pathometry. Part III. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science. 1917;93: 225–240. Available: http://adsabs.harvard.edu/abs/1917RSPSA..93..225R