Since we can assume that zombies not out-number humans by a factor of at least 100 to 1, perhaps as much as 1000 to 1, you might want to consider what this means.
I would assume that Luke and Samantha might be considering this, as might some of the other scientifically directed characters-
For example, we could argue that mankind, while intellectually and techncially superior, is no longer the dominant species on the planet.
Considering that zombie in large numbers can overwhelm people- we can also think of zombies as predators and humans as prey.
The ecological paradigm that the environment exists in a delicate balance has been challenged by different theories.
One theory is that if the environment does exist for long periods in some kind of stable order, those orders are often disrupted by rather chaotic events- catastrophes which may upset the balance.
Consider for instance a fire in a national park may upset the natural balance of plants, herbivores and carnivores. The fire in Yellowstone, the environmental consequences of the Tsunami, the eruptios of volcanos and even oil slicks suggest that while the environment may adapt and "heal" from such damage, this healing is often a time consuming period and that the environment is rarely quite what it was in the past.
- for our characters there should be some realization that the world has dramatically changed and that it will be many years before things get back to anything close to "normal" and never back to how things used to be.
- While the ecological argument that "no animal eats more than it has to" has been disproved by evidence of predators killing purely for sport, another theory holds a different notion that is consistent with the "catastrophe" theory above.
Under this theory - a predator species will hunt and destroy a prey species until the prey species is wiped out- even though this may lead to the long run starvation of the predator species.
If you put a cheetah in with a field of sheep, it will kill every sheep it can regardless of the sheep's ability to replicate itself.
In our situation, the zombies will eat humans until there are no humans left, and then maybe they will starve (as if thaty matters).
What normally saves a prey species is its ability to operate in large numbers to create protective habits or to find refuge. A refuge would allow the prey species a place of safe retreat beyond the ability of the predator species to get.
That said, prey species also need to cater to basic needs- food, water, rest.
Do you have a refuge? How do you account for food, water, rest?
Also what will you do in order to restock your limited supply of guns.
(Remember- there is a big sporting goods/hunting shop in Syndey- just down the road).
A final thought- if the zombie apocalpyse is spreading like a virus, than a virus can mutate due to the environment.