An infant’s immune system doesn’t mature until around 2 to 3 months, assuming the baby is a term baby. If the baby is born prematuredly, the baby's immune system will only start maturing 2 to 3 months after the supposed due date. In those first few months, the immune system — especially cell-mediated immunity — becomes more developed. This is very important in helping a child fight off viruses.This means that a 2-week-old baby’s immune system can’t fight viruses or bacteria nearly as well as a 3-month-old infant’s can.