Mathematical Modelling of Insecurity in Northern Nigeria: The Roles of Elites, Technology and Constitutional Bias

Abstract

This paper constructs and examines a deterministic compartmental dynamical framework to capture insecurity dynamics in Northern Nigeria arising from elite influence, technological facilitation, and constitutional bias. The population is stratified into susceptible individuals, insecure individuals, active violent elites, exposed individuals, technologically enabled actors, and recovered individuals. Fundamental qualitative properties of the model, including positivity, invariant region and boundedness, are established. The insecurity-free equilibrium is derived and its local stability analyzed using the next-generation matrix approach, leading to the formulation of a control reproduction number Rc. Global stability of the insecurity free and endemic equilibria was also carried out. Sensitivity analysis reveals that insecurity transmission and constitutional bias are the most influential parameters sustaining instability, while recovery, institutional reform, and technological disruption significantly reduce persistence. Numerical simulations confirm the global asymptotic stability of the endemic equilibrium when Rc>1, demonstrating the structural persistence of insecurity. The model provides quantitative insights into how governance reforms and social interventions can effectively mitigate insecurity in Northern Nigeria.