What is a hit point? Losing hit points abstract injury. Gaining hit points abstract healing. D&D has no real system for broken bones or failing organs. Everything is boiled down to either hit points (95% of all damage), or ability score damage (rare at best).
The DMG is full of rules for stuff like starvation, dehydration, forced movement, and all sorts of environmental stuff that would kill a normal person, that no DM ever, ever, ever uses. When was the last time you couldn’t get enough sleep? When was the last time your mount died because you rode it to death?
This adventure is intended to explore both ideas. The party are seasoned adventurers afflicted with a disease. Healing magic in any form is no use. No potions, no prayers, no spells can reverse the disease. The party has a short amount of time to make a journey to the cure.
While you can keep the length of the journey a secret, I think it would be more fun for the players to give that to them upfront so they can plan. You throw the wrenches in with your choice of encounters, but the terrain should be at least knowable. They should be expected to traverse deserts, tundras, rivers, grasslands, etc. Use all of the environments. Make starving to death or dehydration a possibility. Force them to scavenge and use survival.
The entire time, secretly track their hit points. In fact, don’t let them know their hit points from the start. If they die, let them keep playing. When they reach the cure, the cure works for the living. The dead find out they’re ghosts. Maybe it’s a shitty thing to do, but this adventure is about the journey more than the destination. Whether they survived or not is kind of irrelevant.
Most of this idea was shamelessly stolen from a video game.