I think all animals, not just cats, are sensitive to moods and illness. In my opinion, cats are very intuitive.

A lot of studies have shown that just being around animals lowers blood pressure & respiration, brings a calmness to the body, relaxes brain activity. Having a beloved pet nearby can speed recovery time for things like heart & back surgery... There are some dogs that are trained to detect cancer & seizures... My snakes seem to know when they just need to be still & drape across my shoulders or rest on my head vs. when I'm ok w/them racing for the floor...