I was struck by several references to "the dog". No name. People usually call their dogs by their names. More than any single point that suggested how severely alienated from each other & the world in general they were.
Clearly the film is metaphorical. No one thinks to ask Martin how he manages to arrange a sickness that baffles the best medical science has to offer. Taking him prisoner made a lot of sense. It's what a person might actually do in those circumstances, but since Farrel's character evidently had leave to kill his own son without legal consequences, why not kill Martin afterwards?
Others have criticized his character for not considering sacrificing himself. I agree. It should have been. But assume for a moment Martin wanted him to survive in order to feel the lose he felt in losing his father, then why not the mother? She coldly suggests they can have more children, but shouldn't her first consideration be to sacrifice herself for the children she already has? Shouldn't the daughter's statement of the joy it would give her to die in order to save the rest of her family have suggested that Nicole might make a similar sacrifice? (I assume the daughter was paraphrasing Iphigenia in her words).