Thesis (MSc)--University of Stellenbosch, 2007. / 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. / AFRIKAANSE OPSOMMING: Terwyl navorsing en bevolkingsopnames oor MIV/VIGS in ontwikkelde lande
goed gevestig is, is daar in Afrika suid van die Sahara slegs beperkte inligting
oor MIV/VIGS beskikbaar. Derhalwe moet daar van modelle gebruik
gemaak word. Dit is weens hierdie feit noodsaaklik om die moontlikhede en
beperkings van modelle goed te verstaan.
In hierdie werk word ´n eenvoudige model voorgelˆe en dit word dan uitgebrei
deur insluiting van aspekte soos stadiums van MIV outwikkeling, tydvertraging
by VIGS-sterftes en risikogroepe in bevolkings. Die analise is beklemtoon
nie die wiskundage vorme nie en ook nie die data nie. Dit is eerder ´n
verkennende studie waarin beide wiskundige metodes en numeriese simula˙sie
behandel word.
Daar is bevind dat insluiting van stadiums op korttermyn tot ho¨er voorkoms
vlakke aanleiding gee. Die gevolgtrekking is dat die primˆere stadium die
siekte dryf. Verder is gevind dat die insluiting van tydvestraging wel die
kurwe van sterfbegevalle sterk be¨ınvloed, maar dit het min invloed op die
verhouding van aangestekte persone. Daar word getoon dat die kenmerkende
gedrag van die meeste epidemi¨e, naamlik `n aanvanklike styging, `n piek en dan `n afname, in die geval van VIGS slegs voorkom as die bevolking dele
bevat met lae risiko.
Die algehele gevolgtrekking word gemaak dat vir goeie vooruitskattings met
sinvolle parameters, op grond van wiskundige modelle, die insluiting van
stadiums, risikogroepe en vertragings benodig word.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/19641 |
| Date | 03 1900 |
| Creators | Lutambi, Angelina Mageni |
| Contributors | Hahne, Fritz, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | xiv, 106 leaves : ill. |
| Rights | Stellenbosch University |
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