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

Abstract

Corruption is a worldwide problem that affects ma ny countries where by individuals loses their rights, lower community con fidence in public authorities, absence of peace and security, misallocation of resources a nd termination of employment. Despite various measures which have been taken by various c ntries to control corruption, the problem still exists. In this paper, we formulate a nd analyze a mathematical model for the dynamics of corruption in the presence of control m easures. Analysis of the model shows that both Corruption Free Equilibrium (CFE) and Cor ruption 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. T he results indicate that CFE is both locally and globally asym ptotically stable when < 1 whereas CEE is globally asymptotically stable when > 1. The normalized forward sensitivity method was used to describe the most sensitive para meters 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 teachin g is effective to corruption control within short time compared to when each control str ategy is used separately. Therefore, this study recommends that more efforts in providin g both mass education and religious teaching should be applied at the same time to cont rol corruption.