Browsing by Author "Kimathi, Mark"

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    Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania
    (Journal of Mathematics and Informatics, 2020-09-11) Danford, Oscar; Kimathi, Mark; Mirau, Silas
    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.
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    Modeling the Effect of Binding Kinetics in Spatial Drug Distribution in the Brain
    (Hindawi, 2021-07-05) Kashaju, Nelson; Kimathi, Mark; Masanja, Verdiana Grace
    A 3-dimensional mathematical model is developed to determine the effect of drug binding kinetics on the spatial distribution of a drug within the brain. The key components, namely, transport across the blood-brain barrier (BBB), drug distribution in the brain extracellular fluid (ECF), and drug binding kinetics are coupled with the bidirectional bulk flow of the brain ECF to enhance the visualization of drug concentration in the brain. The model is developed based on the cubical volume of a brain unit, which is a union of three subdomains: the brain ECF, the BBB, and the blood plasma. The model is a set of partial differential equations and the associated initial and boundary conditions through which the drug distribution process in the mentioned subdomains is described. Effects of drug binding kinetics are investigated by varying the binding parameter values for both nonspecific and specific binding sites. All variations of binding parameter values are discussed, and the results show the improved visualization of the effect of binding kinetics in the drug distribution within the brain. For more realistic visualization, we suggest incorporating more brain components that make up the large volume of the brain tissue.