Mother-to-child transmission of HIV: The retrovirus HIV can be transmitted from mother to child during breastfeeding. But under conditions of poverty or poor hygiene, the alternative to breastfeeding...

Mother-to-child transmission of HIV: The retrovirus HIV can be transmitted from mother to child during breastfeeding. But under conditions of poverty or poor hygiene, the alternative to breastfeeding carries its own risk for infant mortality. These risks differ in that the risk of HIV transmission is the same regardless of the age of the child, whereas the risk of mortality due to artificial feeding is high for newborns but decreases with the age of the child.50 Figure 5.85 illustrates the additional risk of death due to artificial feeding and due to HIV transmission from breastfeeding. Here the lighter curve is additional risk of death from artificial feeding, and the darker curve is additional risk of death from breastfeeding.

For the purposes of this exercise, assume that the additional risk of death from artificial feeding is A = 5 × 0.785t and that the additional risk from breastfeeding is B = 2, where t is the child’s age in months.

a. At what age is the additional risk of HIV transmission from breastfeeding the same as the additional risk from artificial feeding?

b. For which ages of the child does breastfeeding carry the smaller additional risk?

c. What would be the optimal plan for feeding a child to minimize additional risk of death?

d. Write a formula for a piecewise-defined function R of t giving the additional risk of death under the optimal plan from part c.