Do you eat at a deficit when you have (mild) infections

I've got a cold at the moment, first one of the year, what worries me is it's going a lot slower than usual (it could be I caught two consecutive colds and one of them got better really fast though). I'm doubtful it's the calories, but part of me hears my mothers voice telling me to "eat up" to get my strength back (OK! I never had a mother like that, my mother told me "go to school, if you are really ill they will send you home!").

When you have mild infections, colds etc, assuming they don't mess with your appetite (I imagine if you lose your appetite its natures way of saying not to eat), do you still eat your deficit calories?