A Mathematical Model for Banditry Transmission Dynamics with Informant Networks and Optimal Control Interventions

Аннотация

Banditry has become a significant security challenge in Nigeria, particularly in the Northwestern and North-central regions, where armed groups engage in kidnapping, armed robbery, cattle rustling, and attacks on communities and military installations. This study develops a mathematical model for banditry transmission dynamics that incorporates informant networks and special military force interventions. The model, built as a system of nonlinear differential equations, captures the recruitment of susceptible individuals into informancy and banditry, the progression of informants to bandits, and the impact of military interventions. The basic reproduction number $\mathcal{R}_c$ is derived, and it is proven that the banditry-controlled free equilibrium is globally asymptotically stable when $\mathcal{R}_c < 1$. Sensitivity analysis highlights parameters most influencing transmission, including the progression rate of informants to bandits $(\chi)$, rehabilitation rates $(\gamma_1, \gamma_2)$, and the deployment of special military forces $(\tau)$. An optimal control problem is formulated with three time-dependent control measures: education and enlightenment campaigns $(u_1)$, rehabilitation programs $(u_2)$, and special military force deployment $(u_3)$. Using Pontryagin's Maximum Principle, the optimal controls are characterized and numerically solved. Numerical simulations demonstrate that combined intervention strategies significantly reduce informant and bandit populations, achieving up to 90\% reduction in bandits and 78.9\% reduction in informants. The study provides a rigorous framework for understanding banditry dynamics and offers practical insights for improving security interventions and public policy in conflict-prone regions.