The Antichrist will have control of the earth.

.........................Revelation 13:7 says,
"And it was given unto him to make war with the saints and to overcome them: and power was given him over all kindreds, an tongues, and nations."

It seems from this, that he will control the entire earth.

..............In Luke 2:1 Augustus Ceasar made a decree that "all the world should be taxed". This was limited to the Roman world. The expression "all the world" spoke only of the known world.

.............................It didn't include North and South America or many other countries.