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

[摘要] ENGLISH ABSTRACT :Vertical transmission remains a global problem with respect to HIV infectiondynamics. It refers to the transmission of HIV from the mother to child during pregnancy, delivery and breastfeeding soon after birth. In this thesis, weformulated a mathematical model to determine the transmission dynamics ofHIV/AIDS and the general impact vertical transmission of the disease will haveon the spread of HIV/AIDS in Ghana, given that, horizontal transmission is theonly well documented mode of transmission. The model incorporates treatmentof juveniles, adults and both vertical and horizontal transmission of HIV/AIDS.The infection free state and the persistent state are examined. The analysis of themodel is done through the basic reproduction number R0. We proved that, theinfection free state is globally stable when the reproduction number is less thanone. The model is fitted to data obtained on HIV/AIDS from the Ghana HealthService 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 bornwith the disease. Numerical analysis are carried out as well as sensitivity analysis to determine the parameters that influences the model output. Results fromthe sensitivity analysis showed that, the parameters that have most influence onthe model were, effective transmission rate β and treatment rate τ2. We noticedthat increasing β increases R0 and increasing τ2 decreases R0. This suggeststhat, 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 reductionof HIV/AIDS burden in the population.

[发布机构] Stellenbosch University