The main thing killing me is hunger.
try to hold three pieces of food during the first round, eat one find another.
When you reach a desolate map leave immediately if you don't have enough food to scavenge a long period of time, this will allow you to keep a management of inventory.
Only have one weapon if you don't have a backpack, weapons take up space and only will be used in combat or when breaking barrels.
Try to get a military backpack and raid stores in the city, you'll need the space and the stores are the most loot you'll get in city areas.