So most zombie apocalypse stories involve wiping out 99.9% of the human race and having a small minority survive to try and keep living.

But, let's say I want society as we know it to collapse, but I still want a substantial number of people around to keep some of modern life going. However, if there are too many people they would eventually be able to clear out the zombies...

Also, we need to have enough people so that we can keep repopulating both the human population and the zombie population...

So what is the minimum number of people needed to keep a small city running? For the sake of argument, let's say it started off with 250k and I want to cull at least 80%.

What are the essentials that could be covered? (Power, water, sanitation) And how many people would be needed to cover them?

How many people would be needed to handle farming and livestock?

Obviously, need to figure out how many people would be necessary for security, which would probably need the most employees.