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