Apocalyptic Era: Starting from picking up a Bishoujo

I found a girl of unknown origin outside; she claims to be a time traveler from a post-apocalyptic era. Great calamity is imminent, with abominations spreading across the land, human civilization annihilated, and even the world itself shattering, all beyond redemption. As for myself, I am considering how to confine this beautiful girl, who has temporarily lost her powers, within my home.