Plague looks to have hit the spot: it does kill, and it does cause horrific sequelae, but it also survives long enough to spread.
Bubonic/Pneumonic expression probably helps, two forms means two vector-paths. Host of rats/fleas, well rats are pretty hardy, adaptable, and good at both hiding and breeding rapidly. So they can carry long distances in trade goods, and then bust out to exploit local food sources. Or, just move alongside the trade goods by chance, following the inadequate hygene of the road/river camps. (obviously, hiding on boats also works but the silk road was predominantly a land route)
Nothing those pesky humans did was going to interfere until two things happened: they learned some basic hygene, and they learned a couple of low-bar tricks to immunise, and then finally they invented antibiotics.
But I probably have a trick or two up my sleeve to fight back. Lets start with "helping" them make antibiotics less reliable, and then lets think about other strategies..