Physical Danger
Most of the time, epidemiologists are research scientists, and most research is done in controlled environments. So unless your definition of control is loosing an army of contagious moles into your co-worker's cubicle as a joke, it's going to be a fairly risk free operation.
If you're an "out and about" epidemiologist, it might be slightly different. While you could find yourself in communities at risk for a certain infection, you can bet your bacon that you're heading in prepared. Following all protocols when it comes to dealing with infections and handling samples will keep your academic life very risk free.