A Nonlinear Mathematical and Artificial Intelligence Framework for Modeling and Controlling the Insurgency of Unknown Gunmen in South-East Nigeria

The persistent activities of unknown gunmen in South-East Nigeria have generated severe threats to human security, economic stability, and social cohesion. This study develops a nonlinear mathematical framework, augmented with artificial intelligence (AI), to model and analyze the insurgency dynamics in the region. A system of coupled nonlinear differential equations is formulated to represent the interactions among susceptible civilians, aggrieved populations, active armed groups, logistical support networks, and protective security forces. The model incorporates nonlinear recruitment, logistic amplification, and saturation effects to capture the complexity of armed group evolution and security responses. Stability analysis is carried out to derive the violence reproduction number, which serves as a threshold condition for the persistence or decay of insurgency. To complement the analytical framework, AI methods—including natural language processing for event extraction, convolutional neural networks for satellite imagery analysis, and graph neural networks for spatial diffusion modeling—are proposed for real-time parameter estimation, hotspot detection, and predictive forecasting. The integration of reinforcement learning with the nonlinear model is further applied to optimize resource allocation for security interventions. Results from simulations demonstrate that timely intelligence, economic shock mitigation, and targeted security reinforcement can collectively reduce the violence reproduction number below unity, thereby suppressing insurgency growth. The study provides a hybrid mathematical–AI approach that offers both theoretical insights and practical tools for designing effective counter-insurgency strategies in South-East Nigeria.