Masters Degrees (Mathematical Sciences)

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Browsing Masters Degrees (Mathematical Sciences) by Subject "AIDS (Disease) -- Epidemiology -- Mathematical models"

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    Basic properties of models for the spread of HIV/AIDS
    (Stellenbosch : Stellenbosch University, 2007-03) Lutambi, Angelina Mageni; Hahne, Fritz; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: While research and population surveys in HIV/AIDS are well established in developed countries, Sub-Saharan Africa is still experiencing scarce HIV/AIDS information. Hence it depends on results obtained from models. Due to this dependence, it is important to understand the strengths and limitations of these models very well. In this study, a simple mathematical model is formulated and then extended to incorporate various features such as stages of HIV development, time delay in AIDS death occurrence, and risk groups. The analysis is neither purely mathematical nor does it concentrate on data but it is rather an exploratory approach, in which both mathematical methods and numerical simulations are used. It was found that the presence of stages leads to higher prevalence levels in a short term with an implication that the primary stage is the driver of the disease. Furthermore, it was found that time delay changed the mortality curves considerably, but it had less effect on the proportion of infectives. It was also shown that the characteristic behaviour of curves valid for most epidemics, namely that there is an initial increase, then a peak, and then a decrease occurs as a function of time, is possible in HIV only if low risk groups are present. It is concluded that reasonable or quality predictions from mathematical models are expected to require the inclusion of stages, risk groups, time delay, and other related properties with reasonable parameter values.