What problems do David and Rosalind face?

The world that David and Rosalind inhabit is a post-apocalyptic one, where the vast majority of the relatively civilized population known as the Waknuk believe that an apocalyptic event occurred due to God sending a "tribulation" as punishment for mankind's sins. Out of fear of a second tribulation, the government of this new world practices a strict form of fundamentalist Christianity and follows a school of eugenics so strict that a hot religious debate occurs over a tailless dog. People with mutations are killed or banished to the dangerous fringes. David and Rosalind are two members of the Waknuk society who have a mutation that manifests itself as telepathy. They eventually are forced to leave their home for the fringes and have to spend their lives being hunted because of their abnormalities.

David and Rosalind are both "Deviants." They have a genetic mutation that gives them telepathic abilities. The entire Waknuk society is scared of any kind of change to the gene pool that falls outside of what they consider normal. Consequently, the entire society is watchful for any kind of genetic mutation, and the society deals quick and brutal punishments to anybody displaying genetic abnormalities.  David and Rosalind face this problem. If they are discovered, they risk being banished to the Fringes, being sterilized, or even being killed.

If the worst comes to the worst, and you can't save Petra, it would be kinder to kill her than let her go to sterilization and banishment to the Fringes—a lot more merciful for a child. You understand? Do the rest of you agree?

Many of the problems that David and Rosalind face are a result of having the telepathic gene mutation. They are forced to keep their secret, and they must behave in such a way as to not make people suspicious of their gift. They are eventually discovered, and they are forced to run away to the Fringes. The Waknuk people then try to hunt them down, and the people in the Fringes are not welcoming either. Throughout the novel, David and Rosalind are either in hiding or on the run to protect their lives.