Mathematical Modelling of Poor Democratic Governance in Nigeria and Its Implications for National Development

Poor democratic governance continues to constrain sustainable national development in Nigeria; however, most existing studies rely on qualitative or econometric approaches that do not adequately capture the dynamic evolution of governance practices. This study develops a nonlinear compartmental dynamical model to examine the persistence of poor democratic governance and its implications for national development. The population is divided into politically apathetic citizens, participants in poor democratic practices, and advocates of good governance, while a national development index is introduced to explicitly link governance dynamics with development outcomes. Fundamental qualitative properties of the model, including positivity and boundedness of solutions, are established. A threshold parameter, the basic reproduction number R0, is derived and shown to determine whether poor governance dies out or persists. Stability analysis reveals that the poor governance-free equilibrium is globally asymptotically stable when R0< 1, whereas an endemic equilibrium exists and is globally stable when R0> 1. Numerical simulations based on Nigeria-informed baseline parameters drawn from published sources support the analytical results. Normalized sensitivity analysis identifies the transmission of poor governance behaviours and political recruitment as the strongest drivers of persistence, while reform, sanctions, and turnover exert stabilizing effects. The findings highlight the importance of preventive institutional reforms and sustained civic engagement for long-term national development.