An investigation into joint HIV and TB epidemics in South Africa

[摘要] ENGLISH ABSTRACT: This dissertation investigates certain key aspects of mathematical modeling of HIV andTB epidemics in South Africa with particular emphasis on data from a single well-studiedcommunity. Data collected over a period of 15 years (1994 to 2009) in Masiphumelele, atownship near Cape Town, South Africa are used to develop a community-level mathematicalmodel of the local HIV-TB epidemic. The population is divided into six compartments anda 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) coulddecrease not only the HIV prevalence, but also the TB noti¯cation rate. We present amodeling framework for studying the statistical properties of °uctuations in models of anypopulation of a similar size. Viewing the epidemic as a jump process, the method entailsan expansion of a master equation in a small parameter; in this case in inverse powersof the square root of the population size. We derive two-time correlation functions tostudy the correlation between di®erent types of active TB events, and show how a temporalelement could be added to the de¯nition of TB clusters, which are currently de¯ned solelyby DNA type. We add age structure to the HIV-TB model in order to investigate thedemographical impact of HIV-TB epidemics. Our analysis suggests that, contrary to generalbelief, HIV-positive cases are not making a substantial contribution to the spread of TB inMasiphumelele. We develop an age-structured model of the HIV-TB epidemic at a nationallevel in order to study the potential impact of a proposed universal test and treat programfor HIV on dual HIV-TB epidemics. Our simulations show that generalized ART couldsigni¯cantly reduce the TB noti¯cation rate and the TB-related mortality rate in the shortterm. The timescale of the impact of ART on HIV prevalence is likely to be longer. Westudy the potential impact of more conventional control measures against HIV. Guidancefor possible future and/or additional interventions emerge naturally from the results. Weadvocate a reduction in intergenerational sex, based on our ¯nding that 1.5-2.5 standarddeviation in the age di®erence between sexual partners is necessary to create and sustaina major HIV epidemic. A simulation framework is developed to help quantify variancein age-structured epidemic models. The expansion technique is generalized to derive aFokker-Planck equation. Directions for future work, particularly in terms of developingmethods to model °uctuations and validate mixing assumptions in epidemiological models,are identi¯ed.

[发布机构] Stellenbosch University