The role of bistability in the spread and control of HIV in a given community

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The aim of this project is to study the role played by bistability in the spread and control of HIV prevalence in a given community. The phenomenon of bistability is critical for effective control of certain epidemics. Specifically, this study is a review of the theory of bifurcation and its application to epidemics models. In epidemic models, disease transmission depends on a certain threshold quantity (R0) known as the basic reproductive number such that if R <1, the disease — free equilibrium is stable and the disease can be eradicated and unstable when R0 > 1; in which case the disease persists. However several recent studies have shown that, reducing R0 to values less than unity though necessary is not sufficient to control the spread of the disease. A non — linear dynamical system model for model for transmission of HIV infection, which incorporates an anti - HIV preventive vaccine was studied. Numerical simulation for the model implementation confirm that low efficacy of the vaccine is a reason for bistability in the model, so that, the disease persists under such condition even for R <1 it is found however that if the efficacy of the vaccine is high enough leading to P* > P, (where P is the threshold vaccination coverage level), then community wide — eradication becomes possible. Moreover the simulation results also predict that reducing the initial sizes of the subpopulation to a level where could halt the epidemics.
A thesis submitted to the Department of Mathematics Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirement for the Master of Science degree in Mathematics, 2005