This always happens to me too, I think fast food stands like burger stands etc. make guests sick. Try removing them and replace them all with restaraunts. If you haven't unlocked restaraunts, block the entrance to the zoo with stones until they are unlocked. In this way, guests will just leave the zoo and you won't need to care for them. New stuff becomes unlocked monthly or every year if I remember. That passes in about an hour or so.