Pervade – to spread throughout all parts
Persia invaded (pervade) and spread throughout the Middle Eastern lands.
An alternative would be:
They came in person, invading (pervade) and spreading throughout the world.
Examples of pervade in a sentence
Science and technology have come to pervade every aspect of our lives.
The awful smell from the sewage plant seemed to pervade our house.
Within seconds, it seemed the ants started to pervade the abandoned picnic.