06/08/2020

Training for mathematical models during the pandemic.

Foto: Print da ferramenta computacional RobotDance

Reproduction from the IMPA Science & Mathematics blog, from O Globo, coordinated by Claudio Landim.

Claudia Sagastizábal is a researcher at the Institute of Mathematics, Statistics and Scientific Computing (IMECC) at Unicamp and at the Center for Mathematical Sciences Applied to Industry (CeMEAI). She participates in the project "Lives saved in Brazil by social isolation," which estimates the number of lives saved by social isolation in Brazil during the Covid-19 pandemic.

This column was produced for the #ScientistAtWork campaign, which celebrated National Science Day throughout the month of July.

The COVID-19 pandemic has changed our routines and habits. Overnight, social isolation became the most efficient way to combat the transmission of the disease. But where to isolate? How to predict the evolution of COVID-19? Researchers at CeMEAI, the Center for Mathematical Sciences Applied to Industry, have developed the RobotDance computational tool to plan, in a coordinated manner between neighboring municipalities, social distancing measures that allow the economy to function without overwhelming hospitals. To do this, it is necessary to simulate the progression of the disease taking into account the daily travel patterns of the population between cities.

The simulation uses an epidemiological model of virus transmission that relies on parameters estimated from data. The data available since the beginning of the pandemic are divided into two groups. The older data serves to estimate the parameter and define the model. To determine if the model is good, the simulated values are compared to the real values of the second group. If there is not a good fit, the data and the model are revised. In Artificial Intelligence, this process is known as "training the model," and in Statistics, back-testing .

This mechanism isn't unique to applied mathematics, as we all perform backtesting in our daily lives. Who hasn't had the experience of driving on a highway, returning home from work, for example, and, upon seeing the heavy traffic, decided to take an alternative route, exploring previously unknown streets?

In terms of mathematical modeling, we had a perfect model of the route to be taken. It was perfect because it perfectly satisfied our daily need to get to work. Until an external factor, an uncertainty, forced us to rethink the model. Information about new peripheral routes enriched our mental map of the journey. Before this experience, it was as if these alternative routes didn't even exist for us.

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