A novel fractional order model for analyzing counterterrorism operations and mitigating extremism

Abstract

This study examines the profound impact of terrorism on individuals and society by developing a fractional-order mathematical model to analyze and enhance counterterrorism efforts. The model accounts for the persistent and complex nature of extremist behavior, particularly emphasizing the importance of preventing violent extremism before it escalates into terrorism. Real-world data on terrorist activities in Nigeria – specifically from the Boko Haram insurgency – was used to calibrate and validate the model, ensuring its relevance and accuracy. The model reveals that the basic reproduction number ($R_0$) plays a decisive role in determining the long-term success of counterterrorism strategies. Numerical simulations show that terrorist activities decline when $R_0<1$, while they persist or escalate when $R_0>1$. A comprehensive sensitivity analysis further identifies the most influential parameters affecting $R_0$, providing actionable insights into where interventions can be most effective. Parameters related to recruitment, ideological spread, and counter-radicalization efforts were found to have the highest impact. The study concludes by offering strategic recommendations informed by the simulation and sensitivity results, aiming to support the design of more targeted and sustainable counterterrorism policies.