@mathanxiety
I think for the sake of this particular situation, 'abandoned' means a live baby left (usually) in a public place with no means of identification.
Disposed of babies are, presumably, dead and may, or may not, be found eventually. I remember a case of a skeleton found in a chimney back. Grim. I also learned from a programme about foundlings that concealed births often are followed by immediate suffocation. Grim again. But that's not the same as abandonment which is usually done by a single person ie the mother. Not always though.
This particular case doesn't fit the lone teenager model; more an abusive, coercive, possibly incestuous situation which therefore makes it vital that both parents are found.