Dead Season (2012) on Netflix

When a worldwide viral outbreak leads to a plague of zombies scouring the earth for the living, two survivors flee the chaos of America to a remote island, hoping for a chance to start a new life. What they find is unrelenting horror. Beyond the hordes of the flesh-hungry undead, the other people already on the island force the pair into a fight-or-die battle amongst themselves. Armed only with crude weapons, they must descend to savagery and cutthroat tactics just to make it through each day.