That is the harsh truth. Any prepper now living in a high population area will have to have allies. Unless the prepper is living in or has a steel reinforced fortress with no way for mobs to enter AND!!! an air system that cannot be blocked, their fortress and stocks will be easily overwhelmed.
Even a lot of firepower won't help, because mobs will also have guns and will block gun ports and air systems. If nothing else works, the mob will start fires and roast or suffocate the preppers.
The only thing that will work for preppers in high pop. areas is an alliance with other preppers...but it has to be a neighborhood alliance. Even that will be iffy.
The only preppers who can hold out are the ones already living in remote, mountainous areas, and even they will have to have allies.
The mobs from the 'gimme people' will be the first to perish. They will plunder their own first out of desperation. By the time they run out of plunder and they hit the inner suburbs for those neigborhoods the word will be out and won't end well for the zombies..