If Catfish is referring to their cats, then it’s most likely cat flu. Cat flu is caused by either Feline Calicivirus or Feline Herpe Virus, neither of which are zoonotic (they can’t be passed onto humans).

Toxoplasmosis, giardia, ringworm (not actually a worm, it’s a fungus), and quite a few more are zoonotic.

Catfish won’t have to worry about catching anything from their cats :)