Psychosomatic illnesses spread very easily, through the same means other memetic changes spread.

Unfortunately many people mistakenly believe a psychosomatic illness isn't "real" - when professionals tell them "These people have a psychosomatic illness" what they hear is "These people are lying" which is not what was said, and so when the same professionals tell them, "You have a psychosomatic illness" they hear "You are lying" and they're angry - how dare these professionals accuse them of lying! They know it's real!