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.