A threshold delay model of HIV infection of newborn infants through breastfeeding

The breast milk of HIV infected women contains HIV virus particles, therefore children can become infected through breastfeeding. We develop a mathematical epidemiological model of HIV infection in infants, infected children and infected women that represents infection of an infant/child as a series of exposures, by incorporating within-host virus dynamics in the individuals exposed to the virus through breastfeeding. We show that repeated exposures of the infant/child via breastfeeding can cause bi-stability dynamics and, subsequently, infection persistence even when the epidemiological basic reproduction number $$ is less than unity. This feature of the model, due to a backward bifurcation, gives new insight into the control mechanisms of HIV disease through breastfeeding.