The Egyptians usually had a massive food surplus, which made all their side projects (big temples, pyramids, probably something like the dole) possible, and when neighboring areas didn't have their poop in a group, refugees would enter the country. Also, Egypt was intermittently an occupied territory starting with the Hyksos and continuing until, well, the present, since the Arab population is not a native one, it's just been around a long long time, look at that.
Yes. the biggest influx from the Arabian peninsula did not arrive in Egypt slowly over the early centuries. It came with the Muslims armies during their conquest of Egypt between 639 and 645 A.D.
But, I did not understand the purpose of your link at: “been around a long long time, look at that”.