A person is not contagious during the incubation period. A person is mildly contagious when he or she first experiences symptoms. A person is most contagious about 4 days before the onset of the measles rash.Some risk of transmission lasts until about 4 days after the rash starts. person is mildly contagious when he or she first experiences symptoms. A person is most contagious about 4 days before the onset of the measles rash. Some risk of transmission lasts until about 4 days after the rash starts.