In the first episode from the anime Zombie's already exist. And after finishing the anime there's still no explanation about their origins. Is the outbreak cause already revealed in the manga?
With the current information given we do not know the reason of the outbreak.
This might be a potential plot point later on in the story as they do hint to trying to find out the cause, but we wont know till the manga is updated once more. Which might some while as it been on hiatus for quite some time. Is Highschool of the Dead on hiatus again?