First and foremost it is important to understand that bad breath is never contageous. If it was, everyone would have halitosis and it wouldn't be such an issue.
When it comes to vitamin and mineral deficiencies, it is possible but highly unprobable for a child unless severly undernourished, which I doubt is the case here.
I will assume that your 11 year old boy has good oral hygiene and doesn't have allergies or chonic sinus infections.
Here is how you should proceed:
1/ Start by checking your child's tonsils for any accumulation of food particles within the tonsil crypts. They should be swollen.
2/ Ask him if he has stomach pains or constipation. This could be a sign of him having certain bacteria called 'Helicobacter Pylori' that is well known to cause gastro-intestinal disorders.
3/ Another possible cause is Candida infection. Candida is a fungus that can be present in the mouth and eusophagus. With a small flash light, check your child's mouth for any white spots in the mouth, especially in the back of the throat.
4/ Dry mouth is also a common cause of bad breath. Does he have difficulty speaking and swallowing? A sign of dry mouth is the constant presence of tooth carries.
5/ Don't rule out gum disease. Even young children can have periodontal disease.
6/ Is he on any type of medication? Check the notice for secondary effects. Some drugs can cause dry mouth and bad breath.
7/ Hepatic problems. Liver disease is a major cause of bad breath and will usually release an odor of rotten eggs.
Whatever the underlying problem may be, I strongly suggest you take your son to an ENT and a Gastroenterologists first. Take your son's medical history into account when seing your doctor.
