28/12/2020

In a year of pandemic, mathematics took center stage.

Foto: Agência Brasil

Flattening the infection curve, incidence rate, proportion of recovered patients, and serial interval. While these terms were unfamiliar to most of the population a year ago, in 2020 they became extremely familiar. Given the speed with which the Covid-19 pandemic spread, mathematical modeling emerged as an ally in envisioning future scenarios of the disease.

Mathematical models are created to explain and understand a natural phenomenon that can belong to any area of knowledge. In the case of Covid-19, the tool serves to estimate how the disease will spread, the number of infected people, and the percentage of deaths and hospitalizations. Although prone to errors, modeling has been and continues to be an important tool for decision-making and public policies to combat the disease.

Inaugurated shortly after the Spanish flu (1918 and 1920), "mathematical epidemiology," the field that uses this tool, is a consolidated science that separates the population into susceptible, infected, and recovered individuals. Based on these categories, researchers use differential equations to determine the speed at which the virus spreads.

Seeking to convey an optimistic message, a study by Cepid-CeMEAI (Center for Mathematical Sciences Applied to Industry) at USP calculates the number of lives that social isolation can save in Brazil . The survey, with data from Wednesday (16), indicates that the measure can save one life every 0.9 minutes in the next two weeks. The group made adjustments to the SEIR model, which represents the replication rate of the SARS-CoV-2 virus, to find out if it varies over time. The objective is to identify trends in the evolution of the virus's propagation rate and the consequent acceleration or deceleration of the epidemic after the start of the social distancing protocols implemented in March.

Degree of uncertainty in the models

Because these studies are dynamic, creating premises that vary over time and with societal behavior, the models generate distinct results. This has led to some level of public distrust regarding Covid-19 predictions. One of the most widely publicized cases concerning the role of these professionals in the pandemic was a model presented by Imperial College London. The estimate predicted that more than 250,000 people would die if the British government continued to adopt the herd immunity strategy. “Today, this study still receives criticism because the predicted scenario did not happen. But that's precisely its purpose. The UK government took the fight seriously, and the catastrophe was avoided,” emphasized the director-general of IMPA, Marcelo Viana, in an interview with the newspaper O Globo .

The inconsistency in the country's pandemic data was also pointed out by researchers as a difficulty in increasing the accuracy of the models. In an interview with IMPA conducted in April , epidemiologist Claudio Struchiner, from EMAp-FGV, stressed that underreporting and delayed reporting were recurring problems in surveillance systems, and hindered the discussion about the evolution of the pandemic.

Struchiner also pointed out that uncertainty is a common element in projections across various fields, such as climate and economics. "It's not common for researchers to disclose the number of correct and incorrect predictions they've made out of all others, but the need to express uncertainty about the statements made is fundamental."

Visgraf Covid-19 data visualization project

With graphs showing the evolution of the pandemic and its consequences being disseminated en masse to the population, data visualization was another area that came to the forefront in 2020. However, the excessive volume of information about the pandemic, described by some experts as an "infodemic," does not always provide quality material and can hinder the public's understanding of the disease.

Recognizing the essential role that well-done data visualization plays in communication, Visgraf (IMPA's Computer Graphics Laboratory) created "Coronaviz: visualization in times of Coronavirus," an initiative that addresses the topic from the perspective of mathematics and information design through a portal, technical reports, and scientific articles.

“The pandemic has made it more evident how difficult it is for the population to interpret certain types of visualization. A poorly done visualization generates distrust in the reader, while good examples help to encourage civic practice in society,” said Júlia Giannella, who conceived the initiative along with the laboratory's lead researcher, Luiz Velho.