A stage structured model for HIV/AIDS in the presence of vertical transmission: The case of Ghana

 dc.contributor.advisor Nyabadza, Farai en_ZA dc.contributor.author Appaw, Raima Carol en_ZA dc.contributor.other Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. en_ZA dc.date.accessioned 2018-11-26T09:12:17Z dc.date.accessioned 2018-12-07T06:53:43Z dc.date.available 2018-11-26T09:12:17Z dc.date.available 2018-12-07T06:53:43Z dc.date.issued 2018-12 dc.description Thesis (MSc)--Stellenbosch University, 2018. en_ZA dc.description.abstract ENGLISH ABSTRACT :Vertical transmission remains a global problem with respect to HIV infection dynamics. It refers to the transmission of HIV from the mother to child during pregnancy, delivery and breastfeeding soon after birth. In this thesis, we formulated a mathematical model to determine the transmission dynamics of HIV/AIDS and the general impact vertical transmission of the disease will have on the spread of HIV/AIDS in Ghana, given that, horizontal transmission is the only well documented mode of transmission. The model incorporates treatment of juveniles, adults and both vertical and horizontal transmission of HIV/AIDS. The infection free state and the persistent state are examined. The analysis of the model is done through the basic reproduction number R0. We proved that, the infection free state is globally stable when the reproduction number is less than one. The model is fitted to data obtained on HIV/AIDS from the Ghana Health Service in order to estimate, determine and predict current and future prevalence of the HIV/AIDS epidemics. We also determined that, without treatment, pregnant women have high risk of transmitting HIV to their babies. However, with treatment, even if the reproduction number of vertical transmission Rv increases, the disease can still be kept under control and less babies will be born with the disease. Numerical analysis are carried out as well as sensitivity analysis to determine the parameters that influences the model output. Results from the sensitivity analysis showed that, the parameters that have most influence on the model were, effective transmission rate β and treatment rate τ2. We noticed that increasing β increases R0 and increasing τ2 decreases R0. This suggests that, efforts must be intensified by the health policy makers for continuous sustainability and implementation of the disease protocols to reduce the transmission rate and to enrol more people into treatment. This will lead to the reduction of HIV/AIDS burden in the population. en_ZA dc.description.abstract AFRIKAANSE OPSOMMING : Vertikale transmissie bly ’n globale probleem ten opsigte van MIV-infeksie dinamika. Dit verwys na die oordrag van MIV van die moeder na die kind tydens swangerskap, aflewering en borsvoeding kort na geboorte. In hierdie tesis het ons ’n wiskundige model geformuleer om die transmissiedinamika van MIV/- VIGS en die algemene impak van die vertikale oordrag van die siekte sal hê op die verspreiding van MIV/VIGS in Ghana aangesien horisontale oordrag die enige goed gedokumenteerde modus van oordrag is. Die model sluit behandeling in van jongmense, volwassenes en beide vertikale en horisontale oordrag van MIV/vigs. Die infeksie-vry toestand en die aanhoudende toestand word ondersoek. Die analise van die model word gedoen deur die basiese voortplantingsnommer R0. Ons het bewys dat die infeksie-vry toestand wêreldwyd stabiel is wanneer die voortplantingsnommer minder as een is. Die model is gebaseer op data wat op MIV/VIGS verkry word uit die Ghana Gesondheidsdiens ten einde die huidige en toekomstige voorkoms van MIV te bepaal en te voorspel. Ons het ook vasgestel dat, sonder behandeling, swanger vroue ’n hoë´n risiko het om MIV oor te dra aan hulle babas. Maar met behandeling, selfs al neem die voortplantingsnommer van vertikale oordrag, Rv, toe, kan die siekte steeds onder beheer gehou word en minder babas gebore word met die siekte. Numeriese analise word uitgevoer sowel as sensitiwiteitsanalise om die parameters te bepaal wat die uitset van die model beinvloed. Resultate uit die sensitiwiteitsanalise het getoon dat die parameters wat die grootste invloed op die model gehad het die effektiewe oordrag tempo en behandeling koers τ2 is. Ons het opgemerk dat toenemende β die R0 laat toeneem en toenemende τ2 die R0 laat afneem. Dit dui daarop dat die gesondheidsbeleidmakers die intensiteit van die omgewing moet verbeter vir volgehoue volhoubaarheid en implementering van die siekte protokolle om oordragtempo te verminder en meer mense behandeling gee. Hierdie sal lei tot die vermindering van die MIV/VIGS las in die bevolking. af_ZA dc.format.extent xii, 85 pages : illustrations (some colour) en_ZA dc.identifier.uri http://hdl.handle.net/10019.1/104983 dc.language.iso en_ZA en_ZA dc.publisher Stellenbosch : Stellenbosch University en_ZA dc.rights.holder Stellenbosch University en_ZA dc.subject UCTD en_ZA dc.subject HIV infections -- Ghana en_ZA dc.subject AIDS (Disease) -- Ghana en_ZA dc.subject HIV infections -- Mathematical models en_ZA dc.subject HIV-positive women -- Ghana en_ZA dc.subject AIDS (Disease) -- Prevention -- Ghana en_ZA dc.title A stage structured model for HIV/AIDS in the presence of vertical transmission: The case of Ghana en_ZA dc.type Thesis en_ZA
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