Comparing this movie to the Mad Max series and A Boy and His Dog
MAY CONTAIN SPOILERS!!!!!!!!!!!!!!
The other movies mentioned take place some 10-20 years after a nuclear war, yet everybody is completely healthy, but also feral and without boundaries. In this movie, almost everybody is dead only a few weeks after the bombs dropped.
I'm no scientist, but with Mad Max taking place in Australia, I figured the radiation took much longer to get there, since it's far from where world tensions are.