Deciphering Stability Dynamics of the Banditry Menace Model in Niger State.

Abstract

Niger State has experienced recurrent bandit attacks, kidnapping, and 
mobility restrictions across vulnerable communities. In response, this study 
develops a deterministic nonlinear mathematical model to investigate the 
dynamics of banditry activities, incorporating repentant bandits and 
government intervention efforts. The model further examines the stability 
properties governing banditry dynamics in Niger State. The population is 
partitioned into seven classes, with preventive and reactive control 
measures that include detention of captured bandits, rehabilitation of 
repentant bandits, and government interventions aimed at preventing 
susceptible individuals from being recruited or kidnapped. The bandit-free 
equilibrium and bandit-persistence equilibrium states are established. The 
effective reproduction number, which serves as the threshold parameter, 
is derived using the next-generation matrix approach and used to quantify 
the level of banditry activities. When the effective reproduction number is 
less than one, banditry activities die out from the dynamical system, 
whereas values greater than one indicate persistence of banditry within the 
system. The local asymptotic stability of the bandit-free equilibrium is 
characterized using the Jacobian matrix method, while the local asymptotic 
stability of the bandit-persistence equilibrium is similarly established 
through the Jacobian matrix method. Numerical results demonstrate that 
banditry is effectively curbed when the effective reproduction number is 
below one and persists otherwise. The model provides a mathematical basis 
for evaluating integrated security, socioeconomic, and rehabilitation 
interventions in Niger State. Furthermore, detention of captured bandits, 
reinforced by rehabilitation of repentant bandits, significantly outperforms 
lethal measures in preventing susceptible individuals from being kidnapped 
under the specified preventive and reactive intervention strategies 
considered.