Department of Physics

Permanent URI for this community

https://scholar.sun.ac.za/handle/10019.1/229

Browse

Browsing Department of Physics by Subject "AIDS (Disease) -- South Africa -- Epidemiology"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    An investigation into joint HIV and TB epidemics in South Africa
    (Stellenbosch : Stellenbosch University, 2009-12) Pretorius, Carel Diederik; Muller-Nedebock, Kristian; Welte, Alex; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: This dissertation investigates certain key aspects of mathematical modeling of HIV and TB epidemics in South Africa with particular emphasis on data from a single well-studied community. Data collected over a period of 15 years (1994 to 2009) in Masiphumelele, a township near Cape Town, South Africa are used to develop a community-level mathematical model of the local HIV-TB epidemic. The population is divided into six compartments and a system of di®erential equations is derived to describe the spread of the dual epidemic. Our numerical results suggest that increased access to antiretroviral therapy (ART) could decrease not only the HIV prevalence, but also the TB noti¯cation rate. We present a modeling framework for studying the statistical properties of °uctuations in models of any population of a similar size. Viewing the epidemic as a jump process, the method entails an expansion of a master equation in a small parameter; in this case in inverse powers of the square root of the population size. We derive two-time correlation functions to study the correlation between di®erent types of active TB events, and show how a temporal element could be added to the de¯nition of TB clusters, which are currently de¯ned solely by DNA type. We add age structure to the HIV-TB model in order to investigate the demographical impact of HIV-TB epidemics. Our analysis suggests that, contrary to general belief, HIV-positive cases are not making a substantial contribution to the spread of TB in Masiphumelele. We develop an age-structured model of the HIV-TB epidemic at a national level in order to study the potential impact of a proposed universal test and treat program for HIV on dual HIV-TB epidemics. Our simulations show that generalized ART could signi¯cantly reduce the TB noti¯cation rate and the TB-related mortality rate in the short term. The timescale of the impact of ART on HIV prevalence is likely to be longer. We study the potential impact of more conventional control measures against HIV. Guidance for possible future and/or additional interventions emerge naturally from the results. We advocate a reduction in intergenerational sex, based on our ¯nding that 1.5-2.5 standard deviation in the age di®erence between sexual partners is necessary to create and sustain a major HIV epidemic. A simulation framework is developed to help quantify variance in age-structured epidemic models. The expansion technique is generalized to derive a Fokker-Planck equation. Directions for future work, particularly in terms of developing methods to model °uctuations and validate mixing assumptions in epidemiological models, are identi¯ed.