A person with diarrhea cannot do his job efficiently. Ideally, this person should receive a work permit in order to recover.
Diarrhea is defined as more than two bowel movements daily or more than usual for that person. There may also be loss of stool consistency with or without mucus or blood. In most cases, diarrhea lasts a few days, but when it lasts for weeks, it may indicate a serious illness, such as a persistent infection, cancer, rotavirus, or an inflammatory bowel disease.
If the preparation cook has diarrhea then that means he is at risk of spreading bacteria in the kitchen from his hands and on the food making others unwell. He needs to go on sick leave and be sent home until he has made a full recovery. It would be unsanitary and go against health and safety regulations if he continued to work.