Recent violent political extremist events in Brazil and epidemic modeling: The role of a SIS-like model on the understanding of spreading and control of radicalism

In this work, we study a simple mathematical model to analyze the emergence and control of radicalization phenomena, motivated by the recent far-right extremist events in Brazil, occurred in 8 January 2023. For this purpose, we considered a compartmental SIS-like model that takes into account only the right electors, for simplicity. The model considers radical and moderated right electors, and the transitions between the two compartments are ruled by probabilities, taking into account pairwise social interactions and the important influence of social media through the dissemination of fake news. The role of the Brazilian Federal Supreme Court on the control of such violent activities is also considered in a simple way. The analytical and numerical results show that the influence of social media is essential for the spreading and prevalence of radicalism in the population. In the presence of such social media, we show that radicalism can be controlled, but not extincted, by an external influence, that models the acting of the Federal Supreme Court over the violent activities of radicals. If the social media effect is absent, the radicalism can disappear of the population, and this phenomenon is associated with an active-absorbing nonequilibrium phase transition, like the one that occurs in the standard SIS model.