Boy, too bad Infect and Proliferate already exist, eh?
Personally, I think the key points of the disease should be how it's contagious, and dangerous. Most people
probably don't want to get it. But, there should also be a gameplay reason for it to go around (and maybe some people DO want it, or at least, want to spread it).
However, the problem with making counters (or statuses or whatever) inherently lethal to the creatures themselves is that it kills out all the hosts too fast, making it hard to get that spreading gameplay. So, with that in mind...
Sickly Spreader 
Creature - Carrier
Sickly Spreader enters the battlefield plagued.
(Creatures dealt combat damage by plagued creatures become plagued. At the end of their turn, players lose 1 life for each plagued creature they control.)2/1
It's just kind of a 'status', similar to exert. If it were IRL, I could even see punch-out markers getting included. Since each creature is only either plagued/unplagued I don't think it's that hard to track. You could retool it to include counters I guess, but I stayed away from that to limit math/tracking.
It's... sort of a downside mechanic? but it means cards can also key off the status without being
too parasitic since it'll probably jump around to other creatures all on its own (similar in my mind to how you can play one Monarch card by itself and introduce the mechanic to the game all on your own). Stuff like:
Plague target creature (as a spell, or activated ability)
a Hypocondriac - If CARDNAME becomes plagued, sacrifice it.
Creatures you control can't become plagued / Creatures you control stop being plagued.
As long as CARDNAME is plagued, <buff>.
Plague lord - Plagued creatures cause their opponent to lose an additional life at the end of each of their turns.
"You may plague CARDNAME", or, "You may plague an unplagued creature you control" as a sort of Kicker
Protection from plagued creatures
CARDNAME doesn't (or Creatures you control don't) cause you to lose life for being plagued.