A man in a Saudi hospital has pneumonia. The patient in the room next door gets sick, and before anyone realizes what is happening he infects seven others, each of whom infects at least one more. An outbreak is born. A detailed investigation of the viral illness first detected last year in Saudi Arabia has revealed the chilling ease with which the virus can spread to ill patients in the hospital — and its ability to infect some close contacts like hospital staff and family members who were in good health. A report on the investigation published Wednesday in The New England Journal of Medicine pinpointed the time it takes for a person to get sick after being exposed to the virus, a median of 5.2 days.