Mathematical models for the dynamics of health related risks associated with alcoholism and its control strategy in Tanzania

A Thesis Submitted in Fulfilment of the Requirements for the Degree of PhD Degree in Mathematical and Computer Science and Engineering of the Nelson Mandela African Institution of Science and TechnologyAlcoholic behavior has continually posed health challenges in many communities for decades. Referring to Tanzanian situation, this study presents a more realistic model for the dynamics of health risks associated with alcoholism. The model considered a population proportion that has social cultural protection from alcohol consumption. In the context of this study, such protec tion emanated from religious beliefs practiced in the country. Three versions of the model were analyzed considering different model analysis scenarios: the basic model, fuzzy logic model, and optimal control model. The equilibria of the basic model were obtained and their stability analysis was performed. The Next Generation Matrix (NGM) approach was used to compute the basic risk reproduction number of the basic model. The risk free equilibrium point of the ba sic model was proved to be globally asymptotically stable whenever the basic risk reproduction ratio was less than unit and unstable otherwise. The sensitivity analysis of the basic risk repro duction number of the basic model and numerical simulation were carried out. Their results revealed that deliberate intervention strategies and policies focused on discouraging alcoholic behaviors on their onset during initiation stage were more effective than dealing with alcoholic population proportions. The fuzzy logic based model analysis have confirmed this result where uncertainty conditions were assumed in the measure of influence of alcoholic individua