Stealthy Divine Or Terrifying Natural?

The fact that only those who were harmed by zombies turned into zombies acted as a smoke screen to hide how they infect others. So the gods thought the zombies were spreading the disease through contact, bites, and attacks but the disease was airborne all along. 

The fact that new zombies only appeared in areas attacked by zombies muddled their investigation further and granted the inhabitants a false sense of safety. They put quarantines in place but it didn't stop the appearance of the zombie disease. 

The disease spread so quickly that a council meeting of the gods was called. It wasn't a physical meeting. They are communicating using a rune of communication from the god of knowledge and understanding as a relay to connect all of them. No one wanted to meet physically for fear of transmitting the disease.