Riding on the ambulance for many years you ended up dealing with it sometimes while taking someone to the hospital.
The worse were drunks or drugies. I can think of the many times you get there and they are covered with their own vomit or start moving them and dive for cover when they let loose.
Sometimes it will get to you and you worry you are going to join them in a dual to who will cover the back of the ambulance.
I read in a EMS report that if you feel you will ended up joining the patient has he fills the vomit bucket, garb a towel throw in down in the step well and let loose. After you regain control pick up the towel and put it in a cleaning bag and hope you don't have that far to the hospital to go.