How Liam got sick after finding the mammoth with wasn’t exactly made clear. But my assumption right from the beginning was that it was made clear the mammoth corpse infected anyone who touched it, from Liam and the girl, to the girl’s father and his mate. And that the girl was clearly immune, especially since she stayed resolutely healthy while her father deteriorated as they rambled over the country. It is of course possible I am the only person who came away with that understanding.
I think someone above commented that while they were in the tent, and they came out and blood was outside the tent, this was the father acting out his ‘sickness’. I think this was a misunderstanding, and the blood was instead relating to the father saying there were no polar bears outside, but it turns out they weren’t as safe as he wanted to portray because obviously a polar bear butchered something outside their tent. Or something like that. The father never made it to fullblown ‘mammoth aids’ status, as he was lucid to the point he was murdered by his mate whom he purloined the mammoth with.
As for Elena… remember how when Elena and the girl were in the girl’s father’s house, they’d flick to showing the festering infected corpse of the father ripening in the boiler room? Then the scene where Elena picks up the keys in the hallway, in episode 11, where you hear buzzing of flies and likely see one, but she doesn’t cotton on, and just puts the keys in the door. I think it’s fair to assume the whole point of that scene was to foreshadow Elena getting ‘sick’.