Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania

Abstract

Corruption is a worldwide problem that affects many countries where by individuals loses their rights, lower community confidence in public authorities, absence of peace and security, misallocation of resources and termination of employment. Despite various measures which have been taken by various countries to control corruption, the problem still exists. In this paper, we formulate and analyze a mathematical model for the dynamics of corruption in the presence of control measures. Analysis of the model shows that both Corruption Free Equilibrium (CFE) and Corruption Endemic Equilibrium (CEE) exist. The next generation matrix method was used to compute the effective reproduction number (ܴ ) which is used to study the corruption dynamics. The results indicate that CFE is both locally and globally asymptotically stable when ܴ < 1 whereas CEE is globally asymptotically stable when ܴ > 1. The normalized forward sensitivity method was used to describe the most sensitive parameters for the spread of corruption. The most positive sensitive parameters are κ and ν while the most negative sensitive parameters are α and β . Therefore, the parameters of mass education α and religious teaching β are the best parameters for control of corruption. The model was simulated using Runge-Kutta fourth order method in MATLAB and the results indicate that the combination of mass education and religious teaching is effective to corruption control within short time compared to when each control strategy is used separately. Therefore, this study recommends that more efforts in providing both mass education and religious teaching should be applied at the same time to control corruption.

A Mathematical Modeling Analysis of Racism and Corruption Codynamics with Numerical Simulation as Infectious Diseases

“…The reproduction number is the average number of people that become racist because of the entry of one racial person into a completely susceptible population in the absence of intervention. Moreover, reproduction number utilizes to determining the effect of the control measures and to understand the capability of the corruption to disseminate in the entire community when the control strategies are applied [ 18 ].…”

“…The willingness to act of corruption can be offered from either the receptor side or the provider side [ 15 ]. The act of corruption is found in every sector of society and can affect a small group of people (petty corruption) or affect part or the entire government (grand corruption) [ 18 , 21 ]. Even if most countries including Ethiopia have anticorruption policies as well as measures that are being made to eradicate corruption, it still remains a worldwide problem among the communities [ 15 , 23 ].…”

“…One of the phenomena that can be presented by the mathematical model is the impact and expansion of racism-corruption coexistence among the communities. In this study, we have reviewed a literature done by other scholars to examine the spread and transmission of racism and corruption single existence as infectious diseases with a mathematical modelling approach as stated in [ 8 , 9 , 12 , 15 , 18 , 21 – 23 , 27 , 28 , 30 , 31 , 39 – 45 ], some applied modeling approach for social media addiction [ 20 ], and some used modeling approach for violence [ 6 , 7 , 10 , 11 ]. However, to the best of our knowledge, no one has developed and analyzed a mathematical model on racism-corruption coexistence among individuals in a given society.…”

Mathematical Modeling Investigation of Violence and Racism Coexistence as a Contagious Disease Dynamics in a Community

“…Mathematical modeling has a continuous fundamental role in understanding of the various aspects of dynamical system of real-world situations like [ 17 – 21 ]. It has been formulated and analyzed in different disciplines such as natural sciences as well as social science like [ 1 – 5 , 9 , 22 – 33 ]. Many researchers have applied infectious disease dynamics model to violence, racism, social media addition, corruption, and other social situations.…”

“…Many researchers have applied infectious disease dynamics model to violence, racism, social media addition, corruption, and other social situations. From those researchers, some were applied modeling for social media addiction [ 34 ], some were used modeling for violence [ 1 – 3 , 33 ], some were applied modeling for racism [ 4 , 5 , 25 ], and others used modeling for corruption dynamics [ 22 – 24 , 26 – 28 , 35 – 38 ]. However, to the best of our knowledge, no one has developed and analyzed a mathematical model on violence-racism coexistence on individuals in a given society.…”