08/04/2020

In Folha, mathematics and the eradication of diseases.

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Mathematics is an invaluable tool in the study and control of epidemics. It allows for virtual computer experiments to test different disease containment techniques, something that would be impractical and even unethical in real life, putting people at risk.

One of the first major contributions of mathematics to epidemiology was made in the 18th century by Daniel Bernoulli (1700-1782). The Bernoulli family is the most extraordinary in the history of science, having produced no fewer than eight first-rate mathematicians. They were Swiss, but Daniel was born in the Netherlands and lived in several European countries. His father, Johann, was a mathematics professor, but wanted a more lucrative career for his son: he forced him to study business and medicine. Daniel accepted, on the condition that his father would give him private mathematics lessons. He was very well equipped to contribute to the eradication of smallpox in Europe.

The origin of the disease is unknown, but it is very old: there are smallpox marks on Egyptian mummies from the Tuesdays century BC. It is believed to have entered Europe in the early 1Fridays century and quickly became endemic. The fatality rate was 30%, and many survivors suffered severe after-effects. By the early 18th century, it was killing 400,000 people a year in Europe, and a third of the survivors were blinded.

In the early decades of the 18th century, English doctors began experimenting with a technique called variolation, which consists of inoculating healthy people with fluids from infected individuals to induce the production of antibodies. It had already been practiced in China for centuries, but its use was controversial. Although it reduces the lethality rate to only 1% of those infected, in a few cases it can cause the disease in healthy individuals instead of preventing it.

Daniel Bernoulli developed a mathematical model of the disease, a type of differential equation, to assess whether it would be advantageous to inoculate all newborns in this way, aiming to prevent the subsequent development of the disease. Using the best data available at the time, he concluded that the gain in lives resulting from the immunization provided by widespread variolation would far outweigh any potential losses caused.

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