Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data.
Schistosomiasis commonly known as bilharzia is regarded by W.H.O as a neglected tropical disease. It affects the intestines and the urinary system preferentially, but can harm other systems in the body. The disease is a health concern among majority of the population in Mwea irrigation scheme in Kenya and indeed other tropical countries. This paper documents a deterministic analysis of the effectiveness of non-clinical approaches in the control of transmission of schistosomiasis in the region. A SIR based mathematical model that incorporates media campaigns as a control strategy of reducing transmission of the disease is used. The model considers behavior patterns of hosts as the main process of transmission of the disease. The dynamics of these processes is expressed in terms of ordinary differential equations deduced from the human behavior patterns that contribute to the spread of the disease. The reproduction number R0 and equilibrium points both DFE and EE are obtained. The stabilities of these equilibrium points are analyzed in reference to the reproduction number (R0). Secondary data is used in the mathematical model developed and in the prediction of the dynamics estimated in the model for a period of five years. Numerical simulation was carried out and results represented graphically. The results of the simulation show that the infection decreased from 75108 to about 35000 and the susceptible from 325142 to 50000 respectively in a period of five years. From the analysis, the DFE point is asymptotically stable when R_0<1.Sensitivity analysis of parameters was carried out using partial differentiation. The results show that the sensitivity index of most parameters are inversely proportional to R0 which will reduce schistosomiasis infection. From the results, incorporation of media campaigns as a control strategy significantly reduces transmission of the disease. The results will be useful to MOH to enhance media campaigns to prevent spread of schistosomiasis in Mwea Irrigation scheme and other endemic areas.
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