Zombie 3 (movie, 1988)

When a terrorist's body, infected with a stolen chemical, is recovered by the US military, the corpse is cremated, unintentionally releasing the virus/bacteria into the atmosphere over a small island. Soon the infected populace mutate into flesh-hungry zombies, and a trio of soldiers on leave must team up with a group of tourists and board themselves up in an abandoned hotel as they try to fend off the agile and aggressive living dead.