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

TL;DR

The paper analyzes the emergence and control of radicalization using a simple SIS-like mean-field model that tracks radical ($R$) and moderated ($M$) right-leaning electors. Transitions are governed by $R+M \rightarrow R+R$ at rate $\gamma$, $R \rightarrow M$ at rate $\epsilon$, and $M \rightarrow R$ at rate $\delta$, with the constraint $R(t)+M(t)=1$, leading to the rate equations $\frac{dR}{dt}=\gamma M R-\epsilon R+\delta M$ and $\frac{dM}{dt}=-\gamma M R+\epsilon R-\delta M$. Analytically, the model yields a stationary relationship $R=\frac{\delta M}{\epsilon-\gamma M}$ and a quadratic for $R$ under the normalization, revealing an active-absorbing phase transition at $\gamma_c=\epsilon$ when $\delta=0$; nonzero $\delta$ (social-media effects) destroys this transition and sustains radicalization, with numerical examples showing $R$ rising as $\delta$ increases. The study also shows that increasing $\epsilon$ (deradicalization through judiciary action) can curb radicalism even in the presence of strong social-media influence. Overall, the work provides qualitative insights into how online messaging and legal interventions shape radicalization dynamics and suggests policy levers for control in a minimal, tractable framework.

Abstract

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 January 8, 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.

Figures (3)

• Figure 1: (Color online) Time evolution of the densities of radical ($R$) and moderated ($M$) individuals for fixed $\epsilon=0.2$. The remaining parameters are: (a) $\delta=0.0, \gamma=0.1$; (b) $\delta=0.0, \gamma=0.3$; (c) $\delta=0.1, \gamma=0.1$ (d) $\delta=0.1, \gamma=0.3$.
• Figure 2: (Color online) Stationary densities of radical $R$ (a) and moderated $M$ (b) individuals as functions of the contagion probability $\gamma$. The fixed parameter is $\epsilon=0.2$. We can see that the active-absorbing phase transition is destroyed for nonzero $\delta$, that is a measure of social media effects over moderated individuals.
• Figure 3: (Color online) Stationary density of radicals $R$ as a function of the contagion probability $\gamma$, for typical values of $\epsilon$. The fixed parameters are: (a) $\delta=0.0$ and (b) $\delta=0.5$. We can see that an increase of $\epsilon$, i.e., a higher action of the Federal Supreme Court over extremists, can effectively control the spreading of radicalism, even in the presence of strong social media effects like $\delta=0.5$.