Is the Prince a "madman"? Consider all actions in the story.
There is a suggestion in the story that the Prince has gone mad due to the disease that he has contracted which has caused him to have a long detailed dream or hallucination which is the bulk of the story.
The Prince's hallucination in the midst of the desperate sickness which kills him, he imagines that he has escaped with his friends and gone to the country where they all remain healthy enjoying the fact that they have successfully locked the dreaded red death out of the dwelling.
The Prince is so happy that he gives a masquerade ball where all the rooms are decorated with different colors which are representative of the stages of life.
The Prince's behavior at this party, where he personally confronts the masked stranger, who happens to be the red death in disguise, this action alone suggests that he is mad, however when you look at this in the context of a hallucinatory dream it is easy to understand why the Prince would step up himself and play the hero, and here is the proof:
"The figure then retreats through all seven rooms of the abbey, pursued by Prince Prospero. When the figure reaches the seventh room, it turns to face the Prince, who falls instantly to his death. When the guests rush to seize the figure, they find that, beneath the corpselike costume, there is no "tangible form.''
The experience at the abbey with the 1000 friends must be a dream or hallucination that the Prince has due to his high fever. How else do you explain the 1000 people being accommodated, fed and housed at the abbey? It is not possible, not if the country is ravaged with disease, where would the food come from, the costumes, the decorations, how can he have a party in the middle of a serious epidemic?