SMG Studio

Sorry, 2.a. and the paragraph that follows overlap a little.

A zombie outbreak could come from anywhere, they move in unpredictable directions stopping to feast on the dead.  Zombie apocalypse game mode should follow these 4 rules:

1. Zombie outbreak can happen at any time (Zombie Start)

3. Once bit by a zombie you become a zombie (Zombie Draft)

2. Zombies are unpredictable (Zombie Attack)

4. Zombies wander the earth (Zombie Fortify)

1. Zombie outbreak can happen at any time

Zombie mode on has the potential for one random territory at any random turn including the start to become infected (this means the game could be over before the zombies ever come). all the armies of that territory are now a new zombie ai army, or have a zombie queue of players that control the zombie army.  Zombies cannot form alliances.  After setup, before the draft of each players turn an infection has occurred with probability 1/6.

3. Once bit by a zombie you become a zombie.

The zombie army gains in troops the usual divide by 3 rule, but instead of continent control bonus, they get an infection bonus equal to the number of defender deaths from their previous turn.  They still get to turn in sets of cards representing further outbreak within the general populace.

2. Zombies are unpredictable

2.a. A random Zombie attack

AI

Step 1, a random check determines if the zombies attack or not.  If not the zombies procede to fortify.  

Step 2 A random zombie occupied territory attacks a random adjacent territory with a random number of zombies that auto-blitz.  After this battle repeat Step 1. 

Player

For a player controlled zombie state, auto-blitz is always on.

The zombies spread in allout attack mode.  Always auto-blitz.  A random number of zombies attack a random adjacent territory and also stop attacking randomly, could possibly not attack at all.  At the end of each battle the random zombie attack repeats until the outcome is no attack occurs or time runs out.  The zombie army doesn't care about controlling territories so a zombie army could leave behind a 0 occupied territory.  Zombies are always attacking, therefore attacking a zombie territory can result in a 3v3 dice roll, but zombie awareness level is lethargic at best, therefore this all out attack and lethargy should just counterbalance back to the normal defender dice rule.

4. Zombies wander the earth.

During the fortify phase a random number of zombies move to a random territory, including a territory not zombie occupied, in which case that territory joins the outbreak.  Although, this 'territory joins the outbreak' rule might be OP, tough to say without testing.

Two playstyle suggestions:
1. Eradicate all zombies
2. Story Mode: Reach a territory (Last uninfected area).

2. "Uninfected area" such as isolated Islands, like Greenland, Madagascar, Japan, New Guinea, Philippines, Iceland, or the whole continent of Australia. 
One could begin with a few good men and only by skill (since large armies will be impossible to reach in time to eliminate all zombies) and a bit of luck one will reach the Destination, just as one is about to loose the last few men. "Level 2" could be Playstyle 1: Eradicate All Zombies, Or several missions where you have to save scientists, to begin and work on the previous mentioned cure, and look for other survivors, - whilst securing the perimeters of the"Uninfected area" (which could merge with other nearby sanitised territories?).
Before the game begins, one could see the outbreak and breakdown of civilisation in "Spectator Mode", as I mentioned in my previous comment. 

I thought about it...
If this Zombie Apocalypse was caused by a viral or some other illness, one infantry-unit (or cavalry- or even artillery-units, if your army is large enough), could succumb from this illness each round. One might even had to roll to see if it was converted to a Zombie and/or infected other units and how many. Maybe an initial roll to see if anyone died.