It really depends on your contract from the beginning, this issue REALLY should be discussed before you take any job.
For me, I am willing to watch sick children. I however do not watch children with the stomach flu, severe flu, or strep throat. Essentially, if it's extremely contagious and could keep me out from work both MB and I rather I stay away. I've watched children with ear infections and chest colds, but if your child is vomiting 24/7 I call the parents. Many nannies watch children regardless, that was just my plan since I'm also a student and don't need to miss school.