The disease originated from Hakkar the Soulflayer -- the manager of this very first 20-player raid Blizzard released. Hakkar would cast Corrupted Blood on gamers and it would damage them for about 10 seconds. Players would disperse the effect to other people if they got too close to those infected. After the 10 seconds were done, or players finished the boss battle, the damaging effect was supposed to finish. Only it didn't.
A programming oversight allowed the debuff to disperse beyond the site of the Hakkar boss fight and into the world at large. Much like rats fueled the Bubonic Plague, personalities' trained creatures lacked the Corrupted Blood outbreak. Hunter characters can summon and discount pets to fight at their side at will. Once ignored, all the effects on the pets are paused until it is known as back out again. In effect, the pets could contract Corrupted Blood through the boss fight, disappear then exhibit the symptoms elsewhere in the world map if they were again summoned. There it might spread to other pets and players that came in contact with them.