I have 2 standard ways of dealing with the teeming Egyptian hordes.

The first is very simple: 1) I knock back the Egyptians as quickly as possible (they are the most resilient and frustrating faction in the game anyway), eliminating them from the game at the expense of all other enemies; then 2) I simply allow the cities to revolt and be controlled by rebels. Once the population of these cities grows to the unmanageable point - which doesn't take very long - they result in negative income anyway. So letting them sit there inert until the very end of the game doesn't really hurt that much. I then station a diplomat and a small army in the vicinity to keep other factions from gaining a toehold in the middle of my empire.

If the Egyptians have been particularly nettlesome, I also may employ a more Stalinist - as a previous post so accurately put it - tactic: when the plague strikes in one of my cities, I send an infected unit immediately to Alexandria. The plague is most effective in pruning back the Egyptian population, especially since I can pass it back and forth between Memphis and Alexandria, just as it starts to abate. This tactic will work indefinitely if monitored and managed carefully.