Well, it's a little-known part of law, but in the event of public health emergencies (e.g., the 1918 influenza epidemic, Mary Mallon, the 1989 Reston VA Ebola outbreak, 2001-2 anthrax attacks), be they human or veterinary, your Constitutional rights are suspended. There's really no country that does not do such things, either. The gov't can inspect, quarantine, or do whatever else they deem necessary to halt the spread of disease. Generally they use voluntary measures first, but if that doesn't work....
Having seen some of the antics folks get up to when there is a real threat of deadly disease, I am in favor of keeping this exception. Honestly, I've seen it more under-used rather than abused, because people tend to panic when they are informed, however nicely, that there is a disease they need to be concerned about. Panic is practically a recipe for spreading the really nasty diseases.