# Basic properties of models for the spread of HIV/AIDS

Lutambi, Angelina Mageni (2007-03)

Thesis (MSc)--University of Stellenbosch, 2007.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/19641

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