When I'm home sick, I usually spend the time laying on the sofa, watching a movie. The pup is usually the first to get her nose under my blanket, and curl up on my lap (or stretch out next to me). It's as if she's saying: "You're not feeling well, I'll help you take that nap."
The cat, she's different. She'll jump up near my head, and nudge my face with hers, waking me up. It's as if she's saying: "Well, since you're here and all, you might as well pet me. I know that petting makes you feel better..."