I think it has to do with maps too.
If you want to play Zombie apocalypse then play 6-Armed Snowflake. Or 4 Leaf Clover if you want an easy game. Turn off Barbarian Clans mode.
Ranged units are what you need vs. Zombies. Place them in your cities and encampments (if the Zombies haven't destroyed it that is).
Also naval units like Byzantium's Dromon are great too. Cos you can kill Zombies from the coast and never have casualties (unless from regular barbs).
What is key, I've found to controlling Zombies is making sure you build defenses. Barricades and traps. When you build them the AI send a mix of Zombies and regular barbs to pillage the improvements. As a result the Zombies don't get a chance to get too strong.
View attachment 593150
(Portugal on 6 Armed Snowflake, Zombie Defense, Dramatic Ages and Monopolies & Corporations).