Mathematical Terrorology: Rigorous Analysis of the Dual-Predator Lotka-Volterra Model for Nigeria's Counter-Terrorism Dynamics

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 prioritise 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 normalised 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 ({R}X), 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 ({R}P=0.031), state force sustainability is externally dependent ({R}_{Q₁}=0.019), and non-state actors exhibit hyper-resilience ({R}_{Q₂}=9.25). Decomposition of the insurgent resilience term demonstrates that over 99% derives from the radicalization feedback coefficient (ϕ) triggered by security operations, mathematically validating a predator-symbiosis dynamic wherein state deployments inadvertently fuel recruitment pipelines. The system-wide resilience index ({R}sys=0.174) confirms a structurally fragile regime where kinetic attrition alone cannot destabilize non-state actor growth trajectories. Scenario modelling indicates that community-centred interventions reducing ϕby 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.