## Without knowing the epidemiology, the mathematician went there and did it – basic research

From Pedro Lira

Gonçalo Oliveira ventured into biological mathematics and contributed to epidemic research

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Gonçalo Oliveira, mathematician and professor at the Universidade Federal Fluminense, was unfamiliar with biology. Thanks to the Covid-19 pandemic, he began to grapple with this universe. Out of curiosity, he pointed out a problem in the internationally used standard model for combating epidemics. The observation resulted in an article published in the Journal of Mathematical Biology, which the reviewers defined as a “necessary extension of the theory”.

Epidemiology is the science that studies the factors that determine the incidence and distribution of disease in human communities. From the first infected person, the so-called patient zero, it is possible to map epidemics and think about control strategies. The graph – the visual representation of a mathematical model – that modulates epidemics is shaped like a tree: the root is patient zero; The trunk is the first person it infects. The branches are infected the other. The greener the tree, the bigger the problem.

“This logic is based on the principle that the probability of infection is always the same, regardless of the type of contact people have with one another,” explains Oliveira. In other words, the likelihood that no patient will infect their roommate is the same as the contamination of a person they met on the subway, for example. “The assumption simplifies the model, but it is unrealistic,” says the professor.

Oliveira then proposed an adaptation of the model, taking into account different types of interactions and their probabilities for virus transmission. In practice, this new diagram multiplies the trees that model the contagion, all starting from the same root, patient zero. What he did was the same analysis as the previous model, but now the different trees are modeling different types of interactions.

The mathematician’s solution is more complex, but does not imply a much more difficult calculation. For example, in order to determine the average number of infections per infected person, only three pieces of information need to be determined: the transmission probabilities for each type of interaction (chance encounters in public transport, living in work spaces); the average of the average number of interactions of each type per person; and the mean of the square of the average number of interactions of each type per individual.

It may seem complicated to laypeople, but not to brains used to math. “It’s a model that doesn’t depend on many variables. Find simpler trees that model a real epidemic outbreak in a macroscopically accurate way, ”guarantees the professor.

Although Covid-19 inspired the model, it can be used to study other phenomena associated with epidemic modeling, such as: B. “Super-spreaders” – persons who infect a large number of people through contact with many people – and the “super-shedders” – which, highly contagious, end up infecting many people. “This model is suitable for identifying the impact of these numbers on the spread of an epidemic, comparing the two types or even adding them together,” explains the researcher.

The mathematician’s confidence in the model is new. His research area explores geometric objects through physics, it has nothing to do with mathematical biology. “I compared my article to others to see if it was good and did some research to confirm that no one had written this before,” he says. He submitted the study to the reviewers without showing it to the colleagues on site beforehand. “I was afraid to write something trivial,” he admits.

He didn’t realize the relevance of the material until he read the feedback from experts, who not only pointed to corrections but also highlighted the importance of the discovery to research in the field. “One problem that I and many other mathematicians have is thinking that if I do, I’ll only understand one thing. So I went to college and did it, ”he concludes.

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Pedro Lira is a journalist and social media at Instituto Serrapilheira

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