A Mathematical Model of Endemic Corruption, the Nigerian Perspective

Full Length Research Paper

A Mathematical Model of Endemic Corruption, the Nigerian Perspective

^*Etebefia S.O Maliki S.O Etebefia Chris Ese

¹Department of Statistics Federal School of Statistics Enugu State

²Department of Mathematics, Michael Okpara University of Agriculture Umudike, Abia State

³Department of Applied Geophysics Dennis Osadebay University, Asaba Delta State

*Corresponding Author’s Email: steveoghene@gmail.com

Accepted 21 July, 2025

Abstract

In this work, we created and examined a mathematical model that uses a system of nonlinear ordinary differential equations to investigate the dynamical aspects of corruption as a disease. The Jacobian matrix approach is used to examine the stability analysis of the corruption model. We found and examined the corruption-free equilibrium point. The domain where the model is well posed both mathematically and epidemiologically was identified. The basic reproduction ratio was then calculated using the next generation matrix. When the reproduction number is smaller than one, the model's corruption-free equilibrium is locally asymptotically stable. Additionally, we used MatCAD 14 algebra software to conduct numerical simulations. The mathematical model generated a population that is asymptotically stable, meaning that corrupt practices gradually disappear from the population. Additionally, the sensitivity of the model's parameters was calculated; sensitivity indices with negative signs show that the value of R0 falls as the parameters increase, while sensitivity indices with positive signs show that the value of R0 rises as the parameters increase. According to the sensitivity analysis, the parameters with the highest sensitivity are μ, α, β, θ, v, δ, and τ, in that order.

Keywords: Corruption, Nigeria, Mathematical modelling, Endemic and Sensitivity Analysis