translated from Spanish: The day Bernoulli and d’Alembert fought over the mathematical model of a pandemic

It was the 18th century and smallpox wreaked havoc on the population. So much so, it is estimated that it was the direct cause of 1 in 12 deaths in Europe. Vaccines did not yet exist and little was understood about diseases in general.  Surviving smallpox was more of a matter of «luck»: about 1 in 8 infected people died. One of the few hopes was variolization, a rustic infection inoculation procedure – especially newborns – that was practiced in some regions of the East, particularly in India and China. To Europe it was imported from Constantinople, and had some popularity among the most privileged social classes.
If successful, variolization ensured immunity to smallpox for a lifetime. The problem was that 1 in 200 variolized people developed the disease and ended up dying from it. What to do, then: massively variolize the population, condemning almost immediate death to an undespicable percentage of it, or waiting for the «natural course of things» and sticking to a possibly greater number of deaths? 
Switzerland’s Daniel Bernoulli got into this problem. While the most recognized contributions from his extraordinary family of scientists relate to physics and mathematics, Daniel also had interests in physiology and medicine. No one more appropriate than him, then, to solve the dilemma.
At the time, population censuses were almost non-existent. Bernoulli then resorted to a very special document: a complete record of births and deaths in the Polish city of Wroclaw drawn up by another celebrated and multifaceted scientist. It is nothing less than Edmund Halley, universally known for his observations of a comet that today bears his name (and will pass again near Earth in 2061). 
But the data available to Bernoulli were just those: births and deaths, without any allusion to the causes of these (the word «smallpox» is not mentioned anywhere in Halley’s document). Visionaryally, Bernoulli became aware that he needed nothing else and, after hard work, came to a surprising conclusion: if mass variolization was taken, life expectancy increased from 27 years and 3 months to 29 years and 3 months. A gain of more than 10%! By way of comparison, just imagine someone today telling us that it is possible to suddenly increase life expectancy in Chile in several years, and that the recipe is a strategy linked to solving an equation well! 
How did Bernouilli come to its conclusion? To do this, he worked on the basics of two newly matured theories: probabilities and differential equations. He developed the basic knowledge that enabled him to achieve the miracle that mathematics has enabled throughout history: to get ahead of himself through reasoning and calculation to circumstances that may even be beyond our reach. In context, his equations allowed him to broadly reconstruct the Wroclaw population census in the event that all people had been varicosted.
Bernoulli presented his work to the Paris Academy of Sciences in 1760 and obtained an almost unanimous acclaim. However, for strange reasons, this was not to the liking of the great encyclopedist Jean le Rond d’Alembert, who opposed a rather individualistic vision of the social and public health perspective of Bernoulli. Although French made some justified scopes, he also seemed not to fully understand the Swiss’s mathematical arguments, especially those of a probabilistic order. However, as d’Alembert had great political weight in the academy, he kept Bernoulli’s work on file for nearly a decade. In the meantime, he published a work of his authorship that contained conclusions almost opposite to his. 
Bernoulli’s request to variolize the bulk of the population was never applied, first because of d’Alembert’s behavior, and then because a few decades later Englishman Edward Jenner developed the smallpox vaccine. Despite this, his text inspired mathematical epidemiology to be established as a solid discipline in the late 19th and early 20th centuries. This came particularly after R. Ross’ work on malaria (for which he was awarded the Nobel Prize in Medicine in 1902), which he would later mathematically model in conjunction with Hilda Hudson (also famous for his works in algebra and geometry). Peror the definitive consecration took place between 1927 and 1932 with the emergence of the epidemiological models of Scots W. Kermack and A. McKendrick, which today allow us to guide our strategies in the face of infectious outbreaks such as those of COVID-19. 
The current reality is very different from that of the eighteenth century. At the time, the debate on the applicability of variolization was perfectly valid, beyond Bernoulli’s calculations. However, in the contemporary world, where these ethical aspects are heavily regulated, it is difficult to understand the resistance of a non-negligible percentage of the population to vaccination. Moreover, a large part of this rejection now comes from a landmark 1998 article against a specific vaccine (the viral triple, which protects against measles, rubella and mumps), which was subsequently recognised as highly fraudulent and for which its lead author, Andrew Wakefield, was expelled from the UK General Medical Agency.
Science has always been willing to provide solutions to our problems, while being open to point out its own limitations and even its mistakes. It is thanks to her that humanity has managed to contain and eradicate numerous diseases in the past, including smallpox. Once again, it will be rigorous and transparent science that will allow us to begin to overcome the epidemic that affects us today.
Complementary bibliography:
On Bernoulli’s calculations:
Daniel Bernoulli, pioneer of mathematical models in medicine, by Pierre de la Harpe
About the Wakefield case:
The alleged association between triple viral vaccine and autism and rejection of vaccination, by Andreu Segura Benedicto.
Available in http://scielo.isciii.es/pdf/gs/v26n4/especial1.pdf

Original source in Spanish

Related Posts

Add Comment