Asian Basic and Applied Research Journal

Insecurity in South-East Nigeria is characterised by sudden, extreme surges in violent activity that defy explanation by classical linear or epidemic-type models. This study proposes a nonlinear rogue-wave framework that captures these abrupt spikes through modulation instability arising from nonlinear interactions among armed groups, socio-economic stressors, and state responses. Using security incident data from the Armed Conflict Location and Event Data Project (ACLED) and the Nigeria Security Tracker (2015–2025), machine-learning techniques, including Gaussian Process Regression, Support Vector Regression, Long Short-Term Memory networks, and reinforcement learning, are integrated for parameter estimation, early detection, and adaptive control tuning. An optimal non-kinetic control problem is formulated with three time-dependent controls—intelligence-led operations, community engagement, and socio-economic interventions—with optimality conditions derived via Pontryagin’s Maximum Principle. A fractional-order extension incorporating memory effects is developed, yielding q = 0.85 as the optimal fit to ACLED data (Root Mean Square Error 0.042). Numerical simulations demonstrate that the proposed strategies suppress rogue-wave insecurity spikes by 73.4% in theoretical settings, with expected real-world effectiveness of 41–52% given implementation constraints. The machine-learning early-warning system achieves 89.2% accuracy, with an Area Under the Curve of 0.94. Sensitivity analysis confirms the fractional-order parameter’s critical role in modulating system dynamics. This mathematically rigorous, policy-relevant framework offers actionable insights for mitigating extreme insecurity outbreaks in South-East Nigeria through timely, data-driven non-kinetic interventions.