Here are two ideas that i was tossing around.
(note these are only causes for the inection starting).

1. While cleaning up one of the rooms of a governemnt fecility, a janitor is bitten by a dog that is contamminated with a cure for rabies that has backfired from radiation exposure.

2. Same thing happens except it's a type of insect (like a spider or a bee) then it flies out of it's container then stings (and or) bites someone.