Measles. Measles is an extremely contagious illness caused by a virus that replicates in the nose and throat of those infected. Although typically considered a childhood disease, anyone who is not vaccinated can get it. Symptoms such as a red itchy rash, fever, cough and runny nose usually begin appearing a week after exposure and progress in stages over a period of 2-3 weeks. It’s possible for you to be contagious to others for several days before you know you are sick and remain contagious even after the rash disappears.