The respiratory systems of Mustelidae are similar enough to humans that they easily can become a reservoir for human disease or vector for cross-species transmission. We’ve used ferrets in all kinds of respiratory disease research for this reason (particularly flu studies).
https://wwwnc.cdc.gov/eid/article/24/6/17-2114_article
You’re right about livestock more generally though. Avian and swine livestock also pose a huge risk for pandemic disease. But Mustelidae do as well.