Mathematical Modeling and Analysis of Corruption Dynamics in Kenya

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Date
2024-04
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Kenyatta University
Abstract
Corruption, which can be defined as the abuse of public office for private gains, is a complex and multifaceted problem that has negative impacts on a country’s economy, development, and governance. In the presence of corrupt practices, the affected countries have witnessed an upsurge in poverty levels, political instability, limited employment opportunities, the proliferation of debts (old and new), and a host of other challenges. Although some countries have made commendable strides trying to combat corruption, others have achieved minimal progress, and regrettably, despite efforts aimed at eradicating corruption, it still remains remains a persistent issue and especially in Kenya. It’s for this reason that a better understanding of its dynamics is needed to design effective policy interventions to reduce its prevalence and impact. The goal of this study is to use mathematical modeling and analysis to better understand the dynamics of corruption in Kenya, specifically by modeling the spread and dynamics of corruption using an epidemiological approach. The study aims to investigate the existence and stability of the corrupt-free and endemic equilibrium points, determine the parameters that drive corruption, and compute the reproduction number. The methods applied include the use of ordinary differential equations, linearization method by Jacobian Matrix, Lyapunov function, Next Generation Matrix, Normalized forward sensitivity index, and numerical simulation using MATLAB software. The study conducted stability analysis of the equilibrium states by applying linearization, Lyapunov function and Routh-Hurwitz criteria. The findings indicated that the corruption free equilibrium is stable both locally and globally in cases where R0 < 1 as well as the endemic equilibrium being asymptotic stable when R0 > 1. In addition, a sensitivity analysis was conducted to identify the most sensitive parameter that could be strategically manipulated to effectively combat corruption. This study will contribute to a deeper understanding of corruption dynamics in Kenya and inform policy-making and guide anti-corruption efforts. The expected output is to provide insights into the factors that influence the spread and persistence of corruption in a society. The study also identifies strengths and limitations associated with the epidemiological approach to modeling the dynamics of corruption and recommends potential ways of combining different approaches to study this complex and multifaceted problem. The study recommends policies that aim to reduce the benefits of engaging in corruption and increase the costs of engaging in corrupt behavior to effectively address the issue of corruption.
Description
A Research Project Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Masters of Science (Applied Mathematics) in the School of Pure and Applied Sciences of Kenyatta University, April 2024. Supervisors Winifred Mutuku
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