Great question to ask. This excellent book is of course reminiscent in many ways to other great epics such as The Odyssey, which features the archetype of a journey. If we examine what happens to the father and the boy on this journey, we can see that there are situational archetypes that occur to them that are similar to those encountered by epic heroes such as Odysseus. For example, consider the obvious danger that the father and son face so often, in particular, the house they enter when they find the people locked in the basement. Clearly, the way that they are nearly trapped in this house and are kept as food has echoes of when Odysseus and his men are trapped in the cave of the Cyclops. You might also like to think about the way that the father dies, leaving his son to "carry the torch." This could be related to the relationship between Odysseus and his son Telemachus. Archetypal themes such as the perseverance of hope in the face of despair dominate this compelling narrative.
Spoiler alert!!!! Really wish the person who ansered the question warned you that they were going to ruin the whole book.