Modeling and simulation of the spread of radicalization to terrorism: A theoretical and numerical analysis

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Résumé

In this study, we propose a mathematical model for terrorism dynamics by dividing the population into three compartments: (S) susceptible, (E) extremists, and (T) deradicalized. The model is formulated as a system of nonlinear ordinary differential equations, enabling the determination of the radicalization-free equilibrium, the basic reproduction number R0, and the endemic equilibrium. We analyze the stability of these equilibria, showing that if R0<1,, extremists disappear from the population, while if R0>1, they persist. A bifurcation analysis at R0=1 reveals a transition from terrorism-free to endemic behavior as β (the rate of transition from S to E) exceeds a critical threshold. Sensitivity analysis identifies key parameters for counter-terrorism strategies. Numerical simulations, based on the derived equilibria, support the analytical findings, providing insights into the dynamics of radicalization and the effectiveness of intervention measures.

Mots-clés

Basic reproduction number, radicalization free equilibrium, endemic equilibrium, bifurcation analysis, sensitivity analysis