Abstract:
In this theses, we investigate certain key aspects of mathematical modelling to explain the epidemiology of HIV/AIDS, Tuberculosis, Hepatitis B, Tumour,diabetes and stroke at the workplace and assess the potential benefits of proposed control strategies. The compartmental epidemiological modelling approach was used in the formulation of the models on HIV/AIDS, tuberculosis (TB), Hepatitis B (HBv), Tumour and Diabetes pandemic. In each of the cases, the dynamics of the disease was studied according to the various compartments based on the transmission dynamics of the disease. The resulting model in each of the diseases was a system of nonlinear ordinary differential equations. The solutions of the various models were obtained using ODE45 module in MATLAB software built based on Runge-Kutta 4th Order method and the results plotted on graphs. The model on stroke was formulated using fluid dynamics approach where the geometry of the arteries of the employee(s) was used in determining the flow patterns of blood most especially in an occluded internal carotid artery. The resulting model here is a partial differential equation which was solved using the Galerkindiscretisation scheme implemented by the finite element method in MATLAB and the results plotted on graphs. In the case of HIV/AIDS, a combination of intervention strategies including prevention, Education/enlightenment, and HAART treatment was studied showing a great potential to control HIV transmission in the workplace and indirectly improving the productivity of labour force population and also the availability of good labour force. In the TB model, the two strategies employed, optimal education strategy and chemoprophylaxis clearly showed that both controls reduced/minimised the infected workforce population. In HBV, after introducing therapy, the viral load decreased after 10 days. In addition, the number of free virons at the final time tf= 100 (days) in the case with control is less than that without control thereby increasing the efficiency of drug therapy in inhibiting viral production. In tumour disease, the models described how DCs and NK cells of workers, as the innate immune system, and CD8 + T cells, as the specific immune system, affect the growth of the tumour cell population in the body of workers. In the diabetes model, without control, the work force population is lower than that with control. The work force population increased progressively as the controlincreases. As the stenotic height increased, the diameter of the arteries reduced leading to occlusion thereby lowering the blood flow velocity with high blood pressure leading to stroke. The equilibrium analysis showed that, the models were globally and asymptotically stable at both the disease-free and endemic states. The optimal control measure was established alongside with the various strategies for the controls which showed prodigious improvement in the workforce population on the application of the controls.
