A review of mechanistic and data-driven models of terrorism and radicalization

TL;DR

This paper surveys mechanistic and data-driven approaches to modeling terrorism and radicalization, covering compartmental and age-structured dynamics, lattice and network contagion, game-theoretic interactions, self-exciting event processes, and data-driven forecasting using open-source datasets. It highlights how age structure and network topology shape the spread and persistence of extremist ideologies, and how policy interventions—especially early, targeted action—can influence outcomes. Data-centric analyses and machine-learning applications are presented as valuable for forecasting and risk assessment, while emphasizing ethical considerations and the limits of translating models into policy. The work underscores the need for cross-disciplinary collaboration to validate methods, account for online/offline distinctions, and adapt to evolving tactics and technologies in terrorism.

Abstract

The rapid spread of radical ideologies in recent years has led to a worldwide string of terrorist attacks. Understanding how extremist tendencies germinate, develop, and drive individuals to action is important from a cultural standpoint, but also to help formulate response and prevention strategies. Demographic studies, interviews with radicalized subjects, analysis of terrorist databases, reveal that the path to radicalization occurs along progressive steps, where age, social context and peer-to-peer exchange of extremist ideas play major roles. Furthermore, the advent of social media has offered new channels of communication, facilitated recruitment, and hastened the leap from mild discontent to unbridled fanaticism. While a complete sociological understanding of the processes and circumstances that lead to full-fledged extremism is still lacking, quantitative approaches, using modeling and data analyses, can offer useful insight. We review some approaches from statistical mechanics, applied mathematics, data science, that can help describe and understand radicalization and terrorist activity. Specifically, we focus on compartment models of populations harboring extremist views, continuous time models for age-structured radical populations, radicalization as social contagion processes on lattices and social networks, adversarial evolutionary games coupling terrorists and counter-terrorism agents, and point processes to study the spatiotemporal clustering of terrorist events. We also present recent applications of machine learning methods on open-source terrorism databases. Finally, we discuss the role of institutional intervention and the stages at which de-radicalization strategies might be most effective.

Figures (17)

• Figure 1: Terrorist attacks between 1970-2020, from the Global Terrorist Database (GTD) as compiled by the National Consortium for Study of Terrorism and Responses to Terrorism (START). The GTD details more than 200,000 events including bombings, assassinations, and kidnappings. Data is entered upon reviewing news articles, court reports and other sources. Among the most notable groups are: the FARC in Colombia, Shining Path in Peru, the FMLN in El Salvador; the Red Brigades in Italy, the Red Army Faction in Germany, the PIRA in Northern Ireland and the ETA in the Basque country; Boko Haram in Nigeria and Al-Shabaab in Somalia; Hamas, Hezbollah, ISIS, Al -Qaeda and the Taliban in the Middle East; the LTTE and the NPA in South and Southeast Asia, as well as several groups in Jammu and Kashmir.
• Figure 2: Schematics of the radicalization process WRI06. Functional, engaged individuals undergo progressive phases of withdrawal until they set themselves apart from the rest of society. Henceforth, they cultivate a new identity, search for like-minded individuals and prepare for violence. The process culminates in possible terrorist attacks SIL07. Not all individuals will progress through the entire hierarchy: the number of radicalizing individuals decreases as the level of extremism increases, leading to a multi-phase horizontal funnel.
• Figure 3: Estimated age of interviewed subjects at the first indication of radicalization. All were radicalized within the United States, inspired by Al-Qaeda or ISIS, and committed terrorist acts over a period of 16 years after September 11$^{th}$ 2001. Group B (129 individuals) is a subset of Group A (289 individuals) for which more detailed data was available. Breaks indicate that no subjects of that age cohort were included in the study. Although individuals can be radicalized at any age, the process is more common during adolescence and early adulthood. Taken from Ref. KLA18.
• Figure 4: Schematics of the radicalization process according to representative compartment models CAS03CAM13. In panel (a) individuals may progress from a general, non-radical state $G$ towards a hierarchy of susceptibles $S$, recent adherents $E$ and full fanatics $F$. Birth and death are also included. In panel (b) two radical groups $\{E_1, F_1\}$ and $\{E_2, F_2\}$ can originate from the susceptible cohort $S$. The two ideologies interact with adherents moving between recent convert groups $E_1, E_2$. The parameter $q < 1$ indicates how effective groups are at cross-recruitment. The transition $E_2 \to E_1$ is modulated by the full radical cohort $F_1$ and by a percentage of recent converts $q E_1$; the $S \to E_1$ transition is modulated by $E_1 + F_1$ and by some members of the opposite group $q E_2$ who proselytize in favor of their counterparts. Similar arguments hold for $E_1 \to E_2$ and $S \to E_2$. In both panels, $T$ is the total population and $C = T - G$.
• Figure 5: Time dependence of the radical population $\rho_2(t) = \int_{a_0}^{a_1} \rho_2(t,a) da$ arising from Eqs. \ref{['EQ:RHO0']}--\ref{['EQ:BIRTH1']} under irreversible radicalization $C_{\textrm{P}} = 0$. Radical populations oscillate defining 40-year cycles reminiscent of Rapoport's wave theory of modern terrorism RAP02. Other parameters are $a_0 = 5$ years, $a_1 = 55$ years, $C_{\textrm{R}} = 50$, $C_{\textrm{A}}= 12$, $C_{\textrm{D}} = 5$, $\alpha_{\textrm{A}} = \alpha_{\textrm{R}} = 20$ years, $\sigma_{\textrm{A}} = \sigma_{\textrm{R}} = 10$ years; initial conditions are $(\rho_0 (a,0), \rho_1 (a,0), \rho_2 (a,0))=(0.989, 0.01, 0.001)$. Under these parameters, radicalization is aggressive, $C_{\textrm{R}} > C_{\textrm{A}} > C_{\textrm{D}}$, and leads to a buildup of extremists $\rho_2(a,t)$ that depletes the activist pool $\rho_1(t,a)$ until no further recruitment of the general population $\rho_0(t,a)$ is possible. The radical cohort eventually wanes due to aging; the cycle restarts with the next generation.