Mathematical Modelling of Radicalization and Terrorism Dynamics

Abstract

The Central Sahel region faces an escalating terrorism crisis involving complex interactions between violent extremism and population displacement, compounded by climatic vulnerabilities affecting marginalized communities. This study develops a compartmental ordinary differential equation model capturing interactions between susceptible populations, active terrorist networks, and internally displaced persons, analyzed through stability analysis, bifurcation theory, and Sobol's global sensitivity analysis via extensive numerical simulations. The mathematical framework demonstrates well-posed structure with established existence and uniqueness properties, revealing that military interventions alone contribute less than twenty percent to sustainable terrorism reduction, while integrated approaches combining radicalization prevention and de-radicalization programs achieve over eighty percent effectiveness. The basic reproduction number $\mathcal{R}_0$ emerges as a critical threshold parameter with transcritical bifurcation at $\mathcal{R}_0 = 1$ delineating terrorism elimination from endemic persistence regimes, and time-dependent sensitivity analysis indicates optimal strategies require adaptive approaches transitioning from prevention focused early interventions to sustained rehabilitation programs. These findings provide quantitative support for counter-terrorism frameworks prioritizing socioeconomic development over purely military solutions, offering a pathway to sustainable stability in the Sahel.