Understanding population density versus security
Here's is a graphic which depicts population density in the USA.
[link to cache.wists.com
It's easier to download it, then look it zoomed in on your computer. For the sake of argument, think of the peaks as zones of troublesome security in a collapse. The issues of urbanization coupled with fleeing people created a mountain. As you approach the city of interest, the dangerous peak moves sharply higher in an ascent, and as you leave the city, it descends rapidly downward.
On the East Coast, there is a highly congested region of multiple peaks. Moving West, these peaks don't fully decline until Wichita. Moving South there are many zones of low population density as well.
In each case, a urban area will likely temporarily change population density from fleeing people based upon their likely heading.
They may not be the only ones fleeing. Incarcerated criminals may be released (intentionally or not) based upon disaster. You must know the area you are traveling through coupled with information about this possibility. Mentally disturbed people may also be released if personnel leave if there's no one to care for them.
Many people may be fleeing on foot, and the most likely case is that they use existing highways to navigate. Since many may block a road, they could swarm a car passing through. It's highly likely that people will deliberately block the road with other vehicles for this purpose.