Conflict: Man vs. Self, Man vs. Man, Man vs. Nature
A well represented theme within the story is the idea of internal and external conflict.
In the case of external conflict (specifically man vs. nature), Ann is forced to remain contained within the confines of the valley, as the "deadness," or radiation poisoning, has spread to the surrounding areas. If she leaves her valley, she will die from radiation sickness.
In conflicts of "man vs. man," there are many instances in which Ann must run from and/or fight Mr. Loomis in his attempts to run her down and return her to the house. Since he is the only other human character living within the bounds of the story, there is very little "man vs. man" conflict to be found in the story. A man vs. man conflict not regarding Ann could be the standoff between Mr. Loomis and his associate Edward, when Loomis murders Edward for fear of losing the radiation suit.
Regarding the internal "man vs. self" aspect of conflict, Ann has many internal conflicts throughout the story. A good example of this is right at the end of the book as Ann begins to leave. She feels deep inside of herself that she should return and say one last goodbye to Mr. Loomis, though she is warring with the idea of him capturing her, or worse, shooting her as he did Edward. Being the introspective character that we can tell she is, Ann often fights her own internal battles with things like leaving Mr. Loomis when he is sick to go to church, killing Faro, and leaving him behind altogether.
Hope
Throughout the entire story, there are many instances when Ann is left with nothing but hope to depend on. When her family leaves and doesn't return, she can do nothing but hope for their return, or at least for the appearance of another human. When Mr. Loomis becomes gravely sick, Ann has little left but Faro, prayers, and hope to guide her through the time when she is unsure if Loomis will even make it through his illness. And when Ann makes her daring plan to escape and steal the safe suit, she can only hope that the scheme goes through as planned without her being caught or hurt by Mr. Loomis.
Compromise
Concerns of compromise trouble and occupy Ann in particular, as Mr. Loomis tends to be indifferent to her attempts at reconciliation. Ann's compassion shines with great brightness, as even though Mr. Loomis has exhibited reprehensible behavior towards her, she stills feels bad for him. Moreover, she does not want to kill him - even if that comes at the cost of her own security. For example, towards the end of the story, Ann compromises on her opportunity to completely fool and effectively destroy Mr. Loomis. While she tricks him into putting his gun down in their final confrontation and steals his safe suit at the same time, she passes on the chance to shoot him. Her desire and attempts at compromise create a source of resilience in Ann, someone who was always quite careful but now has become daring and confident in her ability to confront danger, especially as it compromises her well-being.
On the other hand, Mr. Loomis with a great deal of irony also expresses some degree of compassion and tempers his anger when Ann walks away with his safe suit (which he killed Edward over) and does not shoot her, which Ann was fully expecting. In fact, he points Ann in the direction that he saw birds flying. With a significant change of heart, Mr. Loomis first compromises on his only chance to leave the valley unscathed (by wearing the suit) and then on his only source of human communication and social interaction (Ann). The ending, though quite satisfactory from Ann's perspective, came at great expense and compromise on the part of Mr. Loomis.
Destruction
The plot centers around a war that has devastated humanity, and it is because of that devastation that Ann is left alone to fend for herself. It is because of that devastation that Mr. Loomis killed Edward, and that he eventually becomes possessive and hostile towards Ann. But it is not just material destruction that affirms the, at times, bleak present that Ann and Mr. Loomis occupy - it is also emotional destruction, particularly as caused by Mr. Loomis, that generates conflict between Ann and Mr. Loomis and eventually leads to the dissolution of any possibility of reconciling their relationship. Mr. Loomis effectively wipes out any possibility for living a peaceful life. The irrationality of his choices - as they are completely against his interests - points to the possibility that he indeed has acquired or become victim to a kind of insanity.
Space
Time and time again, there are incredibly vivid descriptions that O'Brien provides of the position of certain landmarks (the pond, the Kleins' store, the creek, and the barn) which undoubtedly contribute to how the reader understands the way Ann navigates her relationship with Mr. Loomis after he attempts to rape her. It is the geography of the valley upon which Ann exercises a great deal of reflection regarding how she is to prevent Mr. Loomis from finding her cave, how she is to avoid getting caught or hurt by him, and how, in the end, she is to trick him and steal his wagon and safe suit. Conceptualizing space is incredibly important for the reader in order to understand how the plot plays out, how the protagonist-antagonist relationship plays out, how Faro as a dog is at once a friend to Ann but also the greatest threat to her safety (because he can track her location to the cave), how running out to the barn even for a few minutes worries Ann when Mr. Loomis is sick, and why evasion from Mr. Loomis for Ann has only been possible because of her knowledge of the landscape.
Health
The restriction of movements, emotions, actions, and possibilities impressed upon on Ann in particular are a result largely of Mr. Loomis's bad health for the first part of the book. After he regains some strength, Mr. Loomis attempts to impose his rule (and eventually himself) on Ann. But even after Ann leaves, his health is a point of vulnerability not as much for him as it is for Ann, whose compassion and good character invites doubt in her mind about the possibility of removing Mr. Loomis from the picture and restoring her pre-Loomis life. Health in this case acts as a motivator and a source of hope (for Ann as she happily tends to Mr. Loomis) as well as a point of emotional exposure and fragility.
Socialization and Friendship
One of the main reasons why Ann shows so much patience with Mr. Loomis's erratic behavior for such a long time - at the expense of her mental health, physical security, and private property - is because she longs for a person to talk to and interact with. As she nurses the unconscious Mr. Loomis back to health, she reads him a book, holds his hand, and plays him the piano. When the hostile (and healthy) Mr. Loomis (in some sense) coerces Ann to read to him and play the piano, she agrees to. That she is doing something for another person, that someone is asking her to do something for them, sparks a type of communicative event and reality that she has not experienced for quite some time. Ann is incredibly happy to find a friend in Mr. Loomis, even if only temporarily. The same could be said of Faro, who though a dog nonetheless serves as a source of interaction and meaning.
On the other hand - despite attempting to subjugate her under his control, maim her, and rape her - Mr. Loomis wants Ann alive. When she leaves the valley, he wants her to come back: it would mean losing a source of human connection and interaction. The desire, ability, and opportunity to find meaning in other people and instill a sense of belonging in them is quite pronounced in Mr. Loomis in the end.