The mathematics that arose from pandemics


By CAPosts 18 January, 2021 - 09:46am 387 views

Centuries before the Covid-19 crisis, Europe experienced other terrible pandemics that decimated its population, such as the Black Death and the Great Plague of London. In those periods, the mathematics that today is fundamental in the modeling of infectious diseases began to develop: the notion of exponential growth and the differential calculus.

The Europeans who suffered the Black Death in the 14th century, especially between 1347 and 1353, believed that sickness was divine punishment. Some of them took refuge in the churches and others ran towards the lupanares, which experienced an unusual development at the time; the former trying to save their souls and the latter with the desire to enjoy their bodies for the last time. The wealthiest fled to their country houses, away from the urban centers, looking for purer and healthier airs. Something similar happened in the great plague of London in the seventeenth century, magnificently described by Daniel Defoe in his Diary of the plague .

Medical knowledge at both times was quite limited and, in reference to microbiology, non-existent. On the other hand, in 14th century England, the mathematical advance was mainly due to the so-called "Merton calculators", a group of schoolchildren linked to Merton College , Oxford. The main calculators were the British Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton. Bradwardine, who was Archbishop of Canterbury, anticipated the notion of exponential growth, by extending the theory of proportions of Eudoxus of Knidos. PP Bradwardine, also known as Calculator , used this theory to establish a relationship between the speed that a body acquired when apply a force F taking into account the resistance R. He observed that the velocity was proportional to the F / R ratio but in a particular way, corresponding to the logarithm of F / R. Although the concept of logarithm and its inverse, the exponential function did not yet exist at that time, he anticipated the idea - later developed by some members of the Bernoulli and Leonhard Euler family - three centuries.

Exponential growth is an increment that grows every time faster as you go, for example an amount x that doubles at each time interval; soon after, in n steps, it will have grown prodigiously to (2 ^ n ) x . That is what happens in an epidemic with infected people or in a culture of bacteria.

More than 300 years after the calculators, the great plague of London besieged the English capital. Among those fleeing to the countryside was a young Isaac Newton, who dropped out of Cambridge University to take refuge on the family farm. There he developed most of his great scientific contributions on mechanics, gravitation and laid the foundations of differential calculus. Current mathematical models of epidemics are mainly based on differential equations that dictate the evolution of the contingents of susceptible, infected and recovered from the notion of derivative.

All these advances have changed the lives of the planet's inhabitants in a spectacular way and, in particular, our response to epidemics.

In order to arrive at the epidemiological models, the birth of statistics was also necessary, at the hands of the Englishmen Francis Galton and Karl Pearson. And, of course, the scientific knowledge that has allowed us to understand life and identify viruses as the main agents of epidemics, developed by Charles Darwin, Gregor Johann Mendel, James Dewey Watson, Francis Harry Compton Crick and Rosalind Elsie Franklin among others. , accompanied by the corresponding technological developments - optical microscopes, electronic microscopes, computers. These ideas are present in the first deterministic models in epidemics, proposed by Sir Ronald Ross, Anderson Gray McKendrick and William Ogilvy Kermack in the first two decades of the s. XX.

All these advances have changed the lives of the planet's inhabitants in a spectacular way and, in particular, our response to epidemics. The population situation, a determining factor in the advance of a pandemic, has also changed. If in the Middle Ages the spread of the disease was slow - it is said that 2 kilometers per day - and it jumped from one place to another mainly by boats - infested with transmitting rats and fleas - today, an infected person can move in a matter of hours thousands of miles away by taking a plane. In addition, the extraordinary growth of the world population - from some 300 million inhabitants in the year 1000 to 7.8 billion today - has also helped the virus to find real highways of spread in a matter of days.

Other reactions have not changed so much. And, thus, we have seen how the authorities have had to dictate confinement measures to prevent the flight of citizens from the cities to the rural areas. We also attend the parties of the youngest practicing carpe díem, as many of our ancestors did in other times:

Manuel de León, CSIC research professor and founder of ICMAT and Antonio Gómez-Corral, University professor Complutense de Madrid, are authors of the book The mathematics of the pandemic (CSIC-Catarata, 2020)

Café y Teoremas is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT) , in which the researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked its development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems."

Editing and coordination: Ágata A. Timón García-Longoria (ICMAT)

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