Basic premise is a virus hits the middle east. Not sure what it is. A navy ship is out with a scientist who is looking into the origin. Navy thinks they are on a training exercise (and shes tagging along for research) and have radio silence and are unaware whats going on outside of Antarctica or wherever they are. They finally discover that the virus has mutated and has spread global.
World has basically fallen into anarchy. Most of the population is wiped. Govts have fallen. The title "the last ship" makes it seem like they are the only hope (well, they kind of are b/c they were away from the outbreak and the scientist knows enough of how to get a cure going) but there are other people alive. Terrorists, factions that have started their own army, etc etc.
Its pretty cool tho. The virus fucks people up. The naval ship blows shit up. Some cool gunplay and shootouts. THe acting is pretty good so far as well. The story isnt unique at all but so far, its done well enough where I dont care.