Mathematical Modelling of Optimal Strategies for Improving Industrial Productive Population in the Presence of Perverse Diseases Pandemic

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.