Early on, the male main character stumbles across a women with her kids and another man. Implied that the man killed her husband in an 'accident' to get her for himself. Later on when out hunting the man tries to kill the main character, which the main character survives, at which point it is just him and the woman's family.
After that is largely a rebuild/repopulation scenario.
Remember ending when the main character was killed (shot?) by one of his eventual children (either his or from the settlement that they started).
Memory is that it was relatively long.
Suspect the nature of the apocalypse was some kind of contagion, though I think they were able to eventually wander into cities for supplies? Can't remember if zombies were an element.
I think an element of the main character surviving might have been being in the wilderness when the event started.
I think it's been around 5 years since I saw it last.