A GOVERNANCE-DRIVEN MATHEMATICAL MODEL OF INSTITUTIONAL CORRUPTION DYNAMICS IN NIGERIAN UNIVERSITIES: STABILITY AND NUMERICAL ANALYSIS

Abstract

Institutional corruption remains a persistent challenge to the effective functioning of universities, where it can manifest through examination malpractice, procurement irregularities, favouritism, unauthorized financial transactions, abuse of administrative authority and other forms of misconduct. Although mathematical modelling has increasingly been applied to the study of corruption transmission and control, many existing models treat corruption as a homogeneous population-level phenomenon and consequently provide limited representation of the institutional structures through which corrupt practices emerge, remain hidden, are detected and are subsequently rehabilitated. This study develops a governance-driven compartmental model for institutional corruption dynamics in Nigerian universities. The model partitions the institutional population into six mutually exclusive compartments: susceptible individuals. , exposed individuals actively corrupt individuals , hidden or asymptomatic corrupt individuals , detected and sanctioned individuals  and rehabilitated or reintegrated individuals . Governance effectiveness  is incorporated structurally into the corruption transmission, detection and reintegration processes. A nonlinear saturated incidence function is employed to represent institutional interactions while limiting the growth of effective corruption exposure at high levels of corrupt activity. The model is shown to preserve non-negativity and boundedness, and a corruption-free equilibrium is obtained. Using the next-generation matrix approach, a basic corruption reproduction number  is derived as the threshold quantity determining the local stability of the corruption-free equilibrium. When , the corruption-free equilibrium is locally asymptotically stable, whereas  permits the emergence of an endemic corruption equilibrium. Numerical simulations using MATLAB's ode45 solver demonstrate the temporal behaviour of the six compartments. The result shows a progressive decline in active and hidden corruption, while a comparison of governance levels is also shown.  and  demonstrates a substantially faster decline in both active and hidden corruption under the higher governance scenario. The results provide a mathematical framework for examining how institutional governance can modify the transmission, detection and persistence of corrupt practices in university environments.