Hi and welcome.
There is no such scientific route of transmission of infection which cause diarrhea by handling deli section. It mostly transmitted through diet. You might have a chronic bug which is causing the symptoms again and again. I would suggest you to get a stool culture while having diarrhea to identify the cause so that it can be treated accordingly and completely. I would suggest you to keep your gloves on while handling foods and wash your hands thoroughly before eating meals.
Let me know if you have further questions.
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If you are handling raw meat, not washing your hands, and then transmitting this to food you eat, or to your mouth in any way, this can be the cause.
So make sure you are taking the correct precaustions.
Othewise, there are many causes of diarrhea...irritable bowel syndrome
inflammatory bowel disease
So see a GI doctor to get to the bottom of this.
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