Modeling HIV vertical transmission with maternal use of highly active anti-retroviral therapy during breastfeeding with special reference to Mozambique

This research considers two non-linear mathematical models for HIV epidemic that spreads in two populations of variable sizes. Two groups are considered, children population and adult population. A basic HIV model with ver¬tical transmission was first considered, followed by an HIV model with vertical transmission through breastfeeding in the presence of HAART treatment. The models are analysed qualitatively, to determine the factors that contribute on the dynamics of vertical transmission of HIV through breastfeeding. The models exhibit two equilibrium points namely, the disease-free equilibrium and endemic equilibrium point, both locally asymptotically stable. In the modified model, for HIV vertical transmission in the presence of HAART treatment during breast¬feeding, it is found that, if the effective reproduction number 1ZR < 1, the disease free equilibrium is always locally asymptotically stable. If TZ > 1, a unique en¬demic equilibrium exists, this is locally asymptotically stable. The values of ill and 7Ze were found to be equal in terms of the parameters appearing, because this number does not depend on the intervention parameter. Numerical simula¬tions were carried to complement the analytical results in investigating the effect of other factors that drive the dynamics of HIV vertical transmission through breastfeeding. The number of infected children, in the presence of treatment, will be smaller than the number of infected children, when there are no interventions. The rate of transmission through breastfeeding, from infected mothers to their babies, contributes highly on the number of infections in newborn babies.