How on earth would you know that without doing blood work on all snifflers? In the winter that could be VERY pricey and inconvenient. There are over 200 viruses that cause almost the exact same symptoms. Good luck with that!
Well then, better yet, fire anyone who comes to work with a cold. Doesn't have to be the flu. I am so sick of getting sick from sick people infecting my workplace. The coughing, sneezing and slobbering/dripping of germs makes me SICK! Use a precious "sick day" and stay home.