MATHEMATICAL TERROROLOGY: RIGOROUS ANALYSIS OF THE DUAL-PREDATOR LOTKA-VOLTERRA MODEL FOR NIGERIA'S COUNTER-TERRORISM DYNAMICS

Source abstract

Nigeria’s counter-terrorism (CT) landscape exhibits a paradoxical dynamic wherein state security forces and non-state armed groups jointly inflict sustained harm on civilian populations, complicating conventional security metrics that prioritize kinetic suppression over systemic protection. This study formalizes a modified Lotka-Volterra framework that conceptualizes civilians as a prey population and both state and non-state actors as competing predators within a coupled nonlinear ordinary differential equation system. Using a synthetic but empirically calibrated datasets reflective of Northeast Nigeria (2009–2024), we conduct rigorous equilibria, linear stability, and normalized sensitivity analyses, followed by 4th order Runge-Kutta simulations under baseline and intervention scenarios. A critical methodological innovation is the analytical derivation of Population Resilience Coefficients (), which quantify each group’s capacity to absorb perturbations and sustain equilibrium relative to extrinsic suppression and intrinsic recovery rates. Results reveal severe systemic asymmetry: civilian resilience is critically depleted (), state force sustainability is externally dependent (), and non-state actors exhibit hyper-resilience (). Decomposition of the insurgent resilience term demonstrates that over 99% derives from the radicalization feedback coefficient () triggered by security operations, mathematically validating a predator-symbiosis dynamic wherein state deployments inadvertently fuel recruitment pipelines. The system-wide resilience index () confirms a structurally fragile regime where kinetic attrition alone cannot destabilize non-state actor growth trajectories. Scenario modeling indicates that community-centered interventions reducing by 60% yield a 41% reduction in civilian casualties, substantially outperforming precision CT adjustments. The framework shifts CT evaluation from body-count metrics to resilience engineering, providing explicit mathematical thresholds for policy optimization. Findings necessitate a paradigm shift toward feedback disruption, institutional recalibration, and civilian protection as the primary stabilization lever in asymmetric conflict ecosystems.