Track background blur and have layer match

I'm using a partial rotoscope in order to insert an image to blend in with the background I have in my footage. The subject moves around and the auto focus on the camera follows. Which means the background varies in blur. Currently my only way matching the blur of my inserted background to the footage is apply a gaussian blur and manually keyframe that effect to the background.

Is there any way to track the blur of an object, or create a digital camera for it to match the focus and have the subject naturally follow?