Mathematical Modeling and Optimal Control of the Dynamics of an Internal Radicalization Process

This study presents a deterministic system of differential equations to model the internal radicalization process. Unlike previous models, we explicitly incorporate the subpopulation of eligibles, individuals who have experienced negative interactions with state institutions due to factors such as corruption, inequality, and poor governance. This inclusion emphasizes the critical role of good governance in mitigating radicalization. We utilize the barrier theorem to establish the well-posedness of the model and rigorously analyze the asymptotic behavior of solutions based on the basic reproduction number R0. We show that the terrorism-free equilibrium (TFE) is locally and globally asymptotically stable when R0 1. In addition, we introduce three time-dependent controls: counter-terrorism strategies, public service improvement, and awareness campaigns. Using the Fleming–Rishel theorem, we establish the existence and uniqueness of optimal control strategies. By applying Pontryagin’s maximum principle, we derive necessary conditions for the control of terrorism ideology spread. Numerical simulations conducted in MATLAB using the Euler method validate our theoretical findings. Our results strongly suggest that continuous improvement of public services through good governance is crucial to mitigating internal radicalization. In addition, integrated and combined control strategies that involve awareness campaigns, military intelligence, and public service improvement are more effective in eliminating internal radicalization than isolated interventions focused solely on military intelligence or awareness campaigns.