Colloquium discusses the use of mathematics in the fight against Covid.

This is an important moment for mathematics. For the first time, our science is having a major impact on public policies worldwide. These are the words of mathematician Tiago Pereira (ICMC-USP), who participated this week in the round table “Mathematical Epidemiology in the Post-Covid World” at the 33rd Brazilian Mathematics Colloquium . But they also reflect conversations about the impacts of the new coronavirus pandemic on mathematics, which has been a fundamental tool in the fight to control Covid-19.

On Thursday (5), Professor Adam Kucharski from the London School of Hygiene and Tropical Medicine presented a comprehensive overview of how mathematical models help to better predict the behavior of a pandemic and overcome limitations of data and analysis on the evolution of the new coronavirus.

“One of the biggest challenges we face during a pandemic is that we can't accurately track what's happening in real time, only the results of what was happening a few weeks ago based on measurements of that pandemic. And the big problem is that the available data is usually not very good. In every pandemic I've worked on, there's always a problem with data, which is always delayed and incomplete,” said Kucharski, author of the book “The Rules of Contagion: Why Things Spread”.

In the plenary session “Using mathematical models to generate better pandemic insights”, the British researcher cited as an example an analysis done by Imperial College – a British university that has become a reference for studies on Covid-19. The study analyzed a day in which the city of Wuhan, China – where the first official records of cases of the new coronavirus were made – reported 41 cases of people infected with the new coronavirus, and two other countries registered three cases.

Since the proportion of cases in other countries was much higher than the proportion of cases registered in Wuhan, researchers applied a simple mathematical model to investigate whether the numbers in the Chinese city were outdated. Based on an average pattern, they estimated how many people in Wuhan had traveled outside the city that day and where they had gone. Then, they calculated the reverse movement and, from there, estimated how many infected people there were at that moment in Wuhan, applying the proportion to that of three infected people in other countries.

"This was a simple but very powerful calculation, because it showed that there were probably already thousands of infected people in Wuhan at that time, which we were able to confirm days later with the updates."

In his lecture, Kucharski also presented mathematical models that can be applied to individual cases to estimate the variation in transmissibility between individuals, and to analyze the arrival of the Delta variant in the United Kingdom, comparing the evolution of this strain with the British strain among those infected in the country. "The only way to avoid new lockdowns is to be very aware and have very up-to-date data on the virus, and mathematical models are essential for this," he concluded.

And the dialogue between mathematics and other areas and sciences is what can guarantee increasingly up-to-date data so that governments can have a more precise idea of the behavior of the virus in their cities and countries, according to mathematician Tiago Pereira. At the Colloquium, he observed how the pandemic integrated mathematics with other fields with which mathematicians like him do not traditionally work.

“With the pandemic, we started working with people from many different fields around the world, and I think that’s something that’s really here to stay. Especially the dialogue between mathematics and data is a great opportunity for Brazilian institutions.”

Tiago Pereira participated in the roundtable discussion on mathematical epidemiology that the Colloquium brought to the participants of its 33rd edition. The debate also included researchers Gabriela Gomes, from the University of Strathclyde, Scotland; Claudio Struchiner, from the Getúlio Vargas Foundation of Rio (FGV-Rio); Chris Bauch, from the University of Waterloo, Canada; and Sara Del Valle, from Los Alamos National Laboratory, United States.

Sara Del Valle is an example of how mathematics has become essential to public policy. Since 2020, she has been working with the World Health Organization, the New Mexico Department of Health, and the Centers for Disease Control and Prevention (CDC), the U.S. Department of Health agency that has been dictating the preventive measures to be adopted in the country since the beginning of the pandemic.

"We mathematicians tend to gravitate toward more abstract models when we can advise and show governments and politicians what can be done with those models," he said.

Symmetries and groupoids

Also on Thursday (5), mathematician María Amelia Salazar, from the Federal Fluminense University (UFF), presented new questions to the virtual audience about the idea of symmetry. In her outreach lecture “Groupoids, the search for symmetries and beyond”, aimed especially at students who want to start scientific research, María Amelia used the drawing of a butterfly to question our common sense about symmetrical images.

“When we think about symmetry, everyone usually has an intuitive idea of it. When we think that a butterfly is symmetrical, we think that when we draw a line in the middle, it looks identical. The same happens when we think about a square. But it's not always like that,” said Salazar, winner of the 2020 For Women in Science Award , promoted by L'Oréal Brazil in partnership with UNESCO in Brazil and the Brazilian Academy of Sciences. Salazar presented groupoids as a solution option when a group of symmetries is not sufficient.