You won't be alone for very long. Mexico City has twice the population of Los Angeles. They will be the first. Then Chinese will come. Then Russians will come. If only 5-10% of the U.S. population survives, we will not be a world power, or a world consumer. The U.S. will no longer be "useful" to the Europeans and China from an economic standpoint. We will once again be the frontier. If it is a world wide apocalypse, then the invasion will only be refugees from the south. If it is localized to the U.S., then the whole world will come. Power will be restored. Claims will be made to the land. Possibly WW3 over who takes control of what territory. Early on, England and France may set up some posts here claiming to protect us, and then they will begin importing population, just like they did 350 years ago.