A Reaction-Diffusion Framework for Modeling the Dynamics of Insurgency in Nigeria: A Deterministic Compartmental Approach with Spatial and Relapse Effects

Document Type : Regular Articles

Authors

1 Ccc, Apata Kristi, Ori Ap

2 Department of Mathematics, Faculty of Physical Science, University of Ilorin, Ilorin, Nigeria

10.21608/sjsci.2025.398234.1284

Abstract

Insurgency remains a persistent challenge in developing nation Nigeria, where socio-political and economic factors fuel cycles of violence and rebellion. In this study, we develop a deterministic mathematical model to describe the spatiotemporal dynamics of insurgency. The population is partitioned into four interacting compartments; vulnerable individuals, active insurgents, security personnel, and reformed individuals. The model incorporates some important features such as ideological luring, recruitment through peer and cross-class influence, reform mechanisms, relapse into insurgency, and tactical neutralization. Spatial diffusion terms are included to simulate mobility and regional spread via a reaction-diffusion system of partial differential equations. We employ the Finite Difference Method hybridized with Method of Lines (MOL) time-stepping to discretize and simulate the nonlinear system using realistic variable and parameter values associated to terrorism in Nigeria. The model accounts for boundary conditions representing no external migration, and initial conditions are defined spatially. The model provides better understanding into the roles of vulnerability management, deradicalization, and security interventions in mitigating insurgency over time and space in Nigeria. 

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