Weird that you get in trouble for taking a specific number of days off.
My schools have always operated through the idea that you're in trouble if your attendance percentage drops below a certain point.
So, if you're really rather sick for a week, you're fine.
But really, if you're sick, then you're sick.
I think I would much rather have someone who is likely to be vomiting to stay at home rather than to come to school where he could spread his illness.