There was an earlier plague in Roman history in the 160s—Lucius Verus, co-emperor with Marcus Aurelius, campaigned against the Parthians (161-165) and his soldiers picked up the plague in Mesopotamia, bringing it back with them.
The Antonine Plague is believed to have been smallpox and/or measles.
Thanks all — there was also widespread disease during other major expansions of the Empire, including Julius Caesar’s conquest of Gaul. These were probably all different diseases. Some of the ancient epidemics don’t match the description of known diseases and could easily be something that died out completely, for whatever reason.
The animals were there all along during a moderate climate, but they weren't doing well so they didn't get to spread the disease.
People would look around for a cause and notice that a returning army, still living outside, came down with the plague before townsmen.
I wonder if the Romans would have tried to further exploit their victory against the Parthians in that war if that plague hadn’t broke out. It seems their territorial gains were minimal in light of the victory.