Mathematical Modeling and Analysis of Corruption Dynamics in Kenya

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Mathematical Modeling and Analysis of Corruption Dynamics in Kenya

Muthoni F. Muriithi* and Winifred Mutuku
Department of Mathematics and Actuarial Science, Kenyatta University, Kenya
DOI: https://doi.org/10.51584/IJRIAS.2023.8712
Received: 22 June 2023; Accepted: 06 July 2023; Published: 03 August 2023

Abstract: This study presents a mathematical model that aims to study corruption in Kenya. The model is validated both epidemiologically and mathematically, with all solutions demonstrating positivity and boundedness within a meaningful set of initial conditions. By investigating unique corruption-free and endemic equilibrium points, as well as computing the basic reproduction number, we assess the system’s behavior. Our analysis reveals that a locally asymptotically stable corruption-free equilibrium point is achieved when the reproduction number is below one, while a locally asymptotically stable endemic equilibrium point is attained when the reproduction number exceeds one. Simulation results confirm the agreement with analytical findings. This research enhances our understanding of corruption dynamics and provides valuable insights for designing effective anti-corruption strategies in Kenya.

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1. Introduction

Corruption has continued to be a pervasive problem around the globe and more so in Kenya. This vice has seen several studies being conducted with the goal of comprehending it. Globally, the World Bank has established an estimate of the international bribery to exceed 1.5 trillion US dollar. In Kenya, an estimated ksh.608 billion which is an approximate of 7.8% of Kenya’s GDP is lost to corruption yearly [30]. These figures continue to rise and Kenya continues to suffer great loses where based on audit and prosecution results, it was claimed that an approximate of 2 billion Kenya shillings is lost to corruption every day according to a news outlet published by [24]. In Kenya, the efforts to combat corruption have encountered obstacles such as ineffective strategies, opposition from politicians, and an inability to maintain long-term reforms in the public sector. Additionally, there is a lack of awareness regarding effective methods for creating systemic change [22]. The World Bank through the Transparency International [12] has averaged the Corruption Index (CI) in Kenya to be 23.97 points as of 1996 up until 2022. Fighting corruption at an individual level is difficult, but it becomes even more challenging when a country’s systems force individuals to engage with corrupt practices. This is particularly true when corruption is perceived as a means to access resources and opportunities that are otherwise unavailable due to inequality or social exclusion. According to [29], greed strongly motivates and enables corruption, while need creates a vulnerable population prone to corruption. Understanding these dynamics is crucial for developing effective strategies to address the root causes of corruption and combat it.
A study by Kinyanjui [13], shows the effects of corruption can and have been felt in areas such as the life expectancy, education, and income per capita. Corruption is also seen to undermine the fairness of institutions, distorts policies and priorities leading to a damaged credibility of governments. It’s hence clear that corruption is a threat that can become an outbreak if appropriate control measures are not put into place to mitigate it and as Abdulrahman [1] puts it, a population where corruption exists, individuals could be exposed to corruption and later on, may end up being the very corrupt individuals in the society. It’s for this reason that [2] developed a new mathematical model and analysed with unvarying recruitment rate and standard incidence for the transmission of corruption dynamics where an analysis was able to show that if a two-fifths of the individuals engaging in corrupt practices are embarrassed due to social media coverage, most of them will become semi-corrupt which can aid in the control of corruption, though, it may take several years before being achieved. In [26] the authors also proposed a model on corruption dynamics where an epidemiological threshold of the vice, corruption, was observed that was in regards to the approximation of the honest population. Another study [27] presented and analysed the non-linear mathematical model and the model was found to be helpful to society in reduction of the burdens of corruption and the study considered job transfers and suspension as punishments for individuals. Another study focused on increasing minimum wage and the amount of tax revenue to monitor corruption [8].

A study by [14] formulated a model that took into account anti-corruption awareness as well as counselling while in jail as the control measures and from it, a person that would lose immunity obtained via counselling in jail did not directly transfer into being corrupt but instead became susceptible due to the human behaviour. In another research, [4] developed a corruption control model which was extended to incorporate optimal control and the findings obtained showed the corruption level in the population can be minimized if the control approaches of corruption through media or punishments are raised and incorporated.