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

Abstract

Vertical transmission remains a global challenge 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 paper, we formulate a mathematical model to determine the transmission dynamics of HIV/AIDS and the general impact of vertical transmission on HIV/AIDS in Ghana given that horizontal transmission is the only well-documented mode of transmission. The model incorporates the treatment of juveniles, adults and both vertical and horizontal transmission of HIV/AIDS. The infection-free state and the persistent state are examined. The model is analyzed via the basic reproduction number R0. We prove 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 to estimate the current and future prevalence of HIV/AIDS epidemics. We conclude that without treatment, pregnant women have a 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 fewer babies will be born with the disease. Numerical analysis, as well as sensitivity analysis, are carried out. Results from the sensitivity analysis show that the parameters that most influence the model output were, effective transmission rate β and treatment rate τ2. We noticed that increasing β increases R0 and increasing τ2 decreases R0.