I'm pretty sure it depends heavily on exactly what pathogen you're dealing with. So if you don't know for sure, take precautions. (Some can be contagious, but not all.)
As a precaution, I'd avoid close contact with your snake while you're sick- especially wash your hands very well before tending your snake, don't sneeze or cough on him, & keep him away from your face (don't breathe on him, either thru your nose or your mouth). Avoid all unnecessary handling (or being close to him) while you're sick.
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