Just started watching "The Last Ship". I can do spoilers as it's fairly obvious from episode 1. Pandemic virus has killed most of the world, and a US navy ship is unaffected as they haven't seen land in months. The cast and acting can be a little cheesy (like a B movie) but once you get used to that, the story is quite good. There's not a zombie in sight (I do like zombie shows but it's refreshing to watch something slightly different). Each episode reveals a new struggle where the captain and various others must use clever and intriguing strategies to stay alive.
I'd say it's a good mash-up between U-571 (the film), LOST, and to some extent star trek (but without the space ships).