When my oldest gets sick, she ups her total sleep time by a couple hours a day. I just give her a little tylenol and she'll sleep off any illnesses.
DS on the other hand, is pretty much the exact opposite. Last time he was sick (about 1.5 months ago) he was sleeping in 30 minute increments, and he was awake for hours in between these little catnaps. He just came down with a cold this week, and last night DH and I were up with him every 20-60 minutes and he was up for at least 30 minutes each time. This momma is tired!
How do you handle illnesses if your LO sleeps less when they're sick?