There wont be millions leaving the city though. The conflict will engulf everyone. They'll raid stores and factories for weeks then turn on each other.

Small groups might try to venture out but most will be too sick and malnourished to do much of anything. Try not eating for a week and see how far out in the country you want to venture.

If it happens during the winter then forget about it, they're all toast in week. Anyone that leaves the city will be found thawing in the spring.