>>it may seem a little magical.
Yeah, it certainly is a convenient prop. I like post-apocalyptic worlds where everything goes to hell in a handbasket, where characters have no recourse to technological crutches and gimmicks. They are forced to prevail the old fashioned way: by their wits.
But it's your story.
I gotta quibble on calling the antagonist "psychotic". Technically, it seems to me, he's more likely to be a psychopath than a psychotic. That is a distinction with a difference. Psychosis is a disorder so dysfunctional in terms hallucinations and an inability to engage in reality testing that is unlikely that he would be able to pursue her for any extended period. In contrast, psychopaths are fairly lucid, just mad as hell and not going to take it anymore.