How common is encephalitis caused by vaccine allergy?

Exceedingly rare. Extraordinarily rare. In fact, almost unheard of in the literature, vaers reporting system or medical studies involving vaccinations.
Lightning. Statistically speaking, you will be struck by lightning 9-10 times for every such side effect.Unbelievably rare.This is much, much, much, much less than the risk of brain problems caused by the vaccine preventable diseases if allowed to occur.