The infected twin will have blood samples drawn on the first day of each cycle, 2 weeks after the beginning of each cycle, and 4 weeks after each cycle to evaluate immune status, viral load and other safety parameters. The frequency of these blood tests may change as the study progresses. The infected twin will also undergo apheresis immediately before each cycle of infusions and one month later to test the white cells for certain immune features. The number of apheresis procedures may be reduced as the study proceeds.