Is it possible to have another "black death" epidemic in modern times?

Slightly. Coronary artery atherosclerosis has a slight familial tendency, especially if he died young, but this is largely overridden by your own lifestyle choices and to a lesser extent your willingness to take medications for elevated cholesterols / high blood pressure as needed. It can usually be prevented regardless of your heredity.
Look at history. If one reads about the epidemic in europe during the dark ages, it becomes clear that hygiene was not present, and knowledge of rats and fleas eluded the numerous peasants. With modern water treatment approaches and health departments, unlikely this would occur during normal times. But all falls apart if war were to occur.