Short story premise?

Sounds good! I would read it! Some things: are they haunting people, or are they BEING haunted? Your first sentence implies they're ghosts haunting people. I don't think that's what you were trying to get across lol. If I'm correct, I would change it to "For fifteen years, they have been haunted and hunted by a notorious serial killer named Trinity." I like the second option for the last sentence more, however, I would add a comma or colon between "chaos" and "as". That's just a personal preference though. It sounds good as is. :)

This does not sound like a good short story.

It just sounds like the chapter of a book, except you've decided to tell the reader the rest of the book in one quick paragraph. Show me, don't tell me.

I'd also clean up the florid language, while working on the basics.

Take the phrase "crashed in chaos," which implies the world was already in chaos before the crash. I find it likely you mean "crashed into chaos," as the verb crash implies a sharp division.

For fifteen years they have been stalked and haunted by a notorious serial killer called Trinity, their ordeal enduring through the midst of the chaos: a devastating infectious plague that brought humanity to its knees and ended the world. But it is about to reach its end.

If it goes on for 15 years the characters would need to be in their early 30's or older.