After a series of demonstrations and riots rippled across Chilean society in 2019, a team of researchers in Chile and Britain, including economists, mathematicians and physicists, decided to find out if social unrest follows predictable patterns.

For their study, the results of which were published Tuesday in the journal Chaos, scientists combined epidemic models with analytical tools adapted from the physics of disorder.

Adopting the perspectives of social scientists and economists, researchers used their new model to analyze the trajectory of the 2019 social unrest in Chile.

The findings showed the spread of riots today involve highly dynamic processes. According to the study's authors, traditional epidemic models are less able to predict the spread of upheaval than they were several decades ago.

For more than a century, scientists have been using epidemiological mathematical models to study the spread of diseases.

"In the 1970s, this type of methodology was used to understand the dynamics of riots that occurred in U.S. cities in the 1960s," study co-author Jocelyn Olivari Narea said in a news release.

"More recently, it was used to model French rioting events in 2005," said Narea, an assistant professor at Adolfo Ibáñez University in Chile.

One of the most popular mathematical models used to predict the spread of disease is called the SIR epidemiological model. The model separates a population into three groups: susceptible, infectious and recovered individuals.

"Within a rioting context, someone 'susceptible' is a potential rioter, an 'infected individual' is an active rioter, and a 'recovered person' is one that stopped rioting," said study co-author Katia Vogt-Geisse, professor of mathematical biology at Adolfo Ibáñez University. "Rioting spreads when effective contact between an active rioter and a potential rioter occurs."

While studying the inner workings of the SIR epidemiological model, researchers realized the model's mathematics is based on what are called Hamiltonian mechanics. The same mathematical structures define Newton's laws of physics.

"This allowed us to apply well-known tools of the physics of chaos to show that within the presence of an external force, the dynamics become very rich," said co-author Sergio Rica Mery, professor of physics at Universidad Adolfo Ibáñez.

"The external force that we included in the model represents the occasional trigger that increases rioting activity," Ibáñez said.

When the models were tweaked to account for rioting triggers, researchers found the trajectory of the subsequent social disruption was highly influenced by the number of potential rioters and active rioters.

Despite the dynamic processes that have dictated the spread of social unrest during the 21st century, the researchers suggest epidemiological models can still be tweaked and updated to predict the spread of riots and upheaval.

"While you might think that the study of disease transmission and problems of a social nature vary greatly, our work shows epidemiological models of the most simple SIR type, enriched by triggers and tools of the physics of chaos, can describe rioting activities well," Vogt-Geisse said.

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