How long until cockroach disease symptoms disappear?

Not enough info: Cockroaches have been implicated as carriers for multiple different diseases, so it depends on which one you contracted.

Wrong question: There is no true "cockroach disease" but they can trigger asthma. Roaches dwell in sewers and feed on feces and corpses, then deposit organisms on surfaces where you prepare food. There are over 30 illness causing bacteria carried by roaches. Most cause gastroenteritis (vomiting and diarrhea). Some require antibiotics, others resolve on their own. Usually requires large infestation to be a problem