I read that book. The premise was interesting (a better book, IMHO, is “Alas Babylon,” which was written in, I think, the 1950s or early 1960s); however, Forstchen’s habit of having his characters break into uncontrolled weeping over singing old show tunes and other such maudlin swill ruined the story for me.
Alas Babylon was definitely a better written book. I found the Forstchen scenario more terrifying and a more plausible potential threat today.