I agree with the other educators who have responded here: the "Red Death" operates within Poe's short story as both a metaphor for the pervading nature of death and as a reference to real epidemics which caused suffering for mankind.

Death manifests in the form of a person at the story's end to mark the inevitability of its presence. Not even the rich revelers—who attempt to hide themselves away from the spread of sickness—are able to escape the natural conclusion to their mortality. 

However, the "Red Death" does bear some similarities to "consumption" (or "tuberculosis" as we now refer to it), an infectious disease which causes sufferers to experience chest pain, cough up blood, and in some particularly extreme cases, bleed massively. Poe's wife, Virginia, was sick with tuberculosis as he wrote the story, and the disease also stole from him many of his other loved ones—his mother, foster mother, and brother.

The "Red Death" is described within the story as having "[b]lood [as] its Avatar and its seal" and was affiliated with "sharp pains, and sudden dizziness, and then profuse bleeding at the pores, with dissolution." The rapidness with which it spreads and claims its victims also seems to resemble hallmarks of the bubonic plague, which killed 50 million people in the 14th century. So although the "Red Death" itself is fictional, Poe clearly drew inspiration from actual illnesses. 

The red death in the story "The Masque of the Red Death" is probably a reference to tuberculosis, a disease that claimed Poe's mother.  It is marked by coughing up quantities of blood as the victim's lungs become so congested that he cannot breathe and dies struggling for air. That is why he called it the red death, because of the blood.  There was no cure for this disease, also known as consumption, in the past. 

I think that Poe combines the basic idea of TB with the intensity of the Plague symptoms for effect.  People die within a half hour in the story, I think, for dramatic effect.

Now, TB is a disease that people are vaccinated against and in the event of infection, it is treated with antibiotics. It is a bacterial infection and therefore responds to antibiotics.

Given that the author is Poe, it's probably both.  Certainly at the end of the story, The Red Death as personified by the reveler is symbolic of the essence of the disease and death, as it was discovered after the other revellers attacked that it was "untainted by any tangible form." In the first paragraph, however, Poe may be alluding to a particular form of the Bubonic Plague known as the septicemic "Black Death," which killed its victims within a matter of hours.