The only two characters in Poe's story who take any meaningful action are Prince Prospero and the character who embodies the Red Death.
Of the two characters, the Red Death, who obviously walks through the palace spreading disease among the revelers, is essentially a static character in that he does not react to his surroundings or take any affirmative action to change his environment. He simply represents a form of horrible death, and his presence in the story is all that is necessary for him to carry out his purpose:
When the eyes of Prince Prospero fell upon this spectral image (which with a slow and solemn movement, as if more fully to sustain its role, stalked to and from among the waltzers. . . .
Even though the Red Death moves among the dancers, as we know later spreading disease, he doesn't interact with anyone or make any movement that would indicate purposeful behavior.
Prince Prospero, however, is dynamic: not only does he take action to protect himself and his favorite courtiers from the Red Death but also he is described sufficiently for us to understand his character:
. . . Prince Prospero was happy and dauntless and sagacious (that is, happy, brave, and wise). When his dominions were half depopulated, he summoned to his presence a thousand hald and light-hearted friends. . . .
Two important elements of Prince Prospero's character are evident here. First, he is a commanding leader who is able to summon followers to his presence in the midst of an existential crisis. In his ability to command, he is a stereotypical strong leader who is taking some steps to save himself and certain of his subjects. Second, however, one could argue that a leader who abandons his people in the midst of such a crisis is no leader at all. Even though during times of plague in Europe, it was not unusual for wealthy people to seclude themselves in rural areas until a plague disappeared, a true leader would hazard his along with the most vulnerable of his subjects.
That Prince Prospero is a dynamic character is evident by his actions designed to change his situation--the creation of a haven from the Red Death, stamped with his "fine eye for colors and effects" and whose "plans were bold and fiery, and his conceptions glowed with barbaric lustre." In fact, his creation of the palace setting and the entertainment leads some of his followers to think that he's crazy, and people had "to hear and see and touch him" to insure themselves that he was not mad.
After ordering his followers to stop the Red Death so that he can execute him, an order that fails because everyone is afraid to touch the Red Death, Prince Prospero
. . .maddening with rage and the shame of his own momentary cowardice . . .
draws a dagger in order to stab the Red Death, cries out, drops the dagger, and "fell prostrate in death the Prince Prospero."
There are few actions as dynamic as trying to kill someone or something and, true to his commanding and courageous character, Prince Prospero attempts to end this unknown threat. I say "unknown" because, at this point, there is no indication that the Prince understands that the figure of the Red Death is actually Death itself. The Prince is simply trying to eliminate someone who dared to intrude uninvited on his celebration of life.