A mathematical model of insecurity dynamics in Nigeria driven by weak governance and institutional failure

This study develops a deterministic mathematical model to examine insecurity in Nigeria as a structurally reinforced outcome of weak governance and socio-economic vulnerability. The model incorporates a governance feedback mechanism linking institutional breakdown to increased recruitment into insecurity, thereby capturing the cyclical interaction between vulnerability and instability. Analytical results establish a basic reproduction number R₀​ that determines the persistence of insecurity. The insecurity-free equilibrium is stable when R₀ <1, whereas a unique endemic equilibrium exists and is globally stable when R₀​>1. Sensitivity analysis identifies governance failure and recruitment intensity as dominant drivers of persistent insecurity, while recovery and reintegration capacity significantly reduce long-term instability. Numerical simulations further demonstrate that modest improvements in institutional effectiveness can substantially lower endemic insecurity levels. The findings provide a quantitative framework for understanding insecurity as a governance-dependent transmission process and highlight structural reform as essential for sustainable security outcomes and to the best of the authors’ knowledge, this is the first model to incorporate governance feedback in insecurity dynamics in Nigeria.