Promotion of breastfeeding has contributed significantly in that it provides optimum nutrition. However, HIV transmission in breastfed infants can occur through multiple exposures to lower doses of virus. In this talk, we will present a mathematical model with threshold-type delay describing this phenomena. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the disease free equilibrium (DFE) is obtained using a Lyapunov-Razumikhin function. Endemic equilibria (EE) are shown to appear through transcritical bifurcation as well as backward bifurcation of the DFE. The analysis of the EE behavior, through the study of a first order exponential polynomial characteristic equation, concludes to the existence of a Hopf bifurcation and gives criteria for stability switches.