This warning was most likely issued to prevent people from bringing SARS to the USA when they come back from visiting the countries. So the answer is pretty much to stop the spread
Probably gloves and a mask, because the most common transports of the flu, is people geting germs on their hands, which are carried to their mouth. A mask would prevent bodily fluids on the hands from getting in the mouth, and gloves will prevent bodily fluids from adhering to the hands.
