Mathematical Modeling and Optimal Control for Effective Border Management in Counterterrorism

This paper presents a study focusing on border management in a counterterrorism context. It deals with a deterministic system of differential equations that explicitly includes a continuous function γ to model border management by dedicated armed forces. The barrier theorem and the Cauchy–Lipschitz theorem are used to show that the system is well-posed. Then, a locally and globally asymptotically stable terrorism-free equilibrium point is identified using the next-generation matrix. A triple control, two for internal strategies and one for border management, is introduced in the model for the optimal control study. Clearly, this paper shows that border management is an imperative in the fight against terrorism. Particularly, even in a context where terrorism is supposed to spread like an epidemic, (R0>1), good border management can reverse the trend and eliminate the terrorist threat. In addition, it proves that joint actions modeled by triple control provide better results than isolated actions. This analysis is strongly supported by rigorous compartmental analyses and numerical simulations performed using MATLAB's ODE45 solver, the gold standard for integrating ordinary differential equations. It is based on an explicit Runge–Kutta (4,5) formula.