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# The mathematical model ‘made in Tarragona’ that calculates how the covid spreads

Researchers at the Rovira i Virgili University (URV) in Tarragona have developed a more precise mathematical model that calculates how SARS-CoV-2 spreads between people and how it does so depending on whether they are vaccinated or not, predicting the impact of prophylactic measures against an infectious disease.

Faced with the challenge of understanding how infectious diseases behave and how they spread, and specifically the coronavirus, Giulio Burgio, Benjamin Steinegger and Àlex Arenas, researchers from the URV’s Department of Computer Engineering and Mathematics, have created a mathematical model that estimates what impact it can have on the spread of a virus, such as the one that causes covid-19, the rate of contact between vaccinated and unvaccinated.

Researchers have started from the idea that contacts between people are not random, but that they tend to interact with others who have similar sociodemographic and behavioral characteristics, a phenomenon known as homophily. There is also a correlation between certain individual characteristics and attitudes regarding the adoption of prophylactic measures against infectious diseases, that is, protection measures are not always adopted homogeneously among the population, which ends up affecting the ability to control over the spread of diseases.

Vaccination is also not adopted uniformly among the population, either due to structural factors such as the quality of health services, lack of resources or the level of income, education or ethnicity, factors that, according to the researchers, determine how viruses spread. Researchers have cited recurrent outbreaks of measles in some high-income countries, due to anti-vaccine groups, as an example.

Although the current mathematical models work for infections such as measles, with a vaccine that is 100% effective, on the other hand, in cases of influenza or variants of SARS-CoV-2, with vaccines with an efficacy of between 20 and 80% need other models to analyze the impact of vaccination and homophily on the spread of the virus.

The new mathematical model has shown that in a situation of imperfect vaccination efficacy, as is the case with covid, there are different types of propagation dynamics: if the interaction rate between vaccinated and unvaccinated people increases, there is a change in the final attack rate of the disease, causing it to increase or decrease.

This grading provides an additional tool for interpreting epidemiological data. The model they have developed not only serves to predict the impact of vaccines, but can be applied to adopt a wide range of prophylactic measures, such as the use of masks, social distancing or digital contact tracing.

The researchers affirm that the model they have developed “is more realistic”, which makes it possible to help understand the impact of measures that change the structure of contacts between people, and thus implement them in the most appropriate way to the current state of an epidemic. .

• Tarragona
• URV
• coronavirus
• math
• pandemic