A Mathematical Model of Terrorism Dynamics Incorporating Social Media Influence and Recruitment Delay

ABSTRACT A delay differential equation model is proposed to investigate the role of social media in amplifying radicalization and sustaining terrorist activity. The classical –– framework, where , , and represent susceptible, active terrorist, and deserted populations, respectively, is extended by incorporating an explicit media compartment. Media production by active terrorists is modeled using a Holling‐type II functional response, while media‐driven recruitment is represented through a Michaelis–Menten incidence function. A discrete time delay is introduced into the face‐to‐face recruitment process to account for the noninstantaneous nature of interpersonal radicalization. The basic reproduction number is derived and we establish positivity, boundedness, and global existence of solutions in forward time. The terrorist‐free equilibrium is shown to be locally asymptotically stable when and unstable when . Using center manifold theory, a transcritical bifurcation at is established, and conditions for the existence of a stable positive equilibrium are obtained. The coexistence of stable terrorist‐free and positive equilibria is shown to generate bistability and hysteresis. In addition, Hopf bifurcation analysis shows that sufficiently large delays can induce sustained oscillatory dynamics. Numerical simulations and bifurcation diagrams support the analytical findings and suggest that online recruitment may contribute to the persistence of terrorist activity even when offline recruitment is relatively weak. The sensitivity analysis is further complemented by a robustness study demonstrating that the ranking of influential parameters varies across different media recruitment regimes, together with a global uncertainty analysis of the media‐related parameters using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs). In particular, face‐to‐face recruitment dominates under weak media influence, whereas media‐related parameters become increasingly influential as the online recruitment effectiveness increases. The results highlight the importance of coordinated offline interventions and rapid suppression of extremist online content in mitigating long‐term radicalization dynamics.