## Analyzing Corruption Dynamics and Control Measures in Nigeria: A Mathematical Model

Published: 2023-11-18

Page: 493-511

Sunday Nwokpoku Aloke *

Department of Industrial Mathematics and Statistics, David Umahi Federal University of Health Sciences, Uburu, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This article aims to examine the dynamics of corruption and three control measures proposed to combat corruptions in Nigeria system. The dynamics of the corruption model were described by the Susceptible - Exposed - Corrupt - Jailed - Honest (SECJH) model using linear ODEs. The corruption elimination threshold is derived from the reproduction number. The optimal control approach employed the application of Pontryagin's maximum principle, which was used to test the effectiveness of proposed control measures. The numerical simulation of the state and adjoint equations was obtained through the application a numerical approach known as Forward-Backward Sweep method and a MATLAB script written for the implementation of the method through Runge-Kutta fourth order method with the controls repeatedly updated for the varying values of $$\alpha$$ 4. This paper positioned the proposed control measures on three strategies for numerical simulation of the corruption model, the graphical results show the effect of changing $$\alpha$$ 4 on the number of corrupted population by keeping the other parameters constant and It was equally shown that there is a significant increase from strategy A to strategy C. This study shows that compliance with control measures requirements is an effective anti-corruption strategy and a corruption-free society is possible when the proposed control measures are implemented. It therefore advisable that the proportion of individuals adhering to the honest class and control levels in this work should be interpreted and used with caution.

Keywords: SECJH model, corruption, basic reproduction number, pontryagin’s maximum principle, controls

#### How to Cite

Aloke , S. N. (2023). Analyzing Corruption Dynamics and Control Measures in Nigeria: A Mathematical Model. Asian Journal of Pure and Applied Mathematics, 5(1), 493–511. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1896

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