Let’s say the man was throwing up at the hospital the first time he went (pretty likely), or that someone might have come into contact with is blood, saliva, feces, or urine while he was there. It seems pretty likely that this might have happened.
Then this person (or people) go home to their loved ones, go to work, go to restaurants and other establishments, etc., and the disease is spread. Some of those people, or the people with whom they’ve had contact, might also have traveled to other cities or states, spreading it there.
It seems pretty contagious, based on what I’ve read. Even healthcare professionals who are taking extreme precautions are getting sick. Just the fact that someone made it here with the disease, even though they are trying to be vigilant about passengers who are traveling from the disease-riddled countries, is extremely frightening.