Meningitis and encephalitis are inflammations of the linings of the brain and the brain itself (respectively). The normal cause is infection either viral, bacterial or other rare causes such as fungi.
In fact it often causes stomach upset (gastroenteritis) without meningitis but sometimes can cause meningitis in someone exposed to someone with the stomach upset.
You are far more likely to catch this virus from someone with a stomach upset than someone with meningitis and even if you did get it you are more likely to get a stomach upset than meningitis.
So...no need to worry (any more than if you knew he had a stomach upset).
Hope that helps
" An hour with a patient is more valuable than any lab test "