Sometimes there are one are two senior couples in a place like that doing something not directly connected to missionary work, but I haven't heard of anyone being in Egypt. The only Muslim country I know that missionaries are in is Jordan, and again, just couples. They were at one time going to send young men to proselyte to the Christians there, but I don't think they got permission to. They have a pretty vibrant branch in Amman.
I don't think there is any place in the world where there is a lot of LDS missionaries. Utah and Idaho might be an exception. The LDS church tends to exaggerate its own importance.
Egypt is a Muslim country which does not allow Christian proselytism. There is a small branch in Cairo for Mormon expatirate living there. Here's all the info about the LDS church in Egypt from cumorah.com, which isn't much. http://www.cumorah.com/index.php?target=missiology_articles&story_id=31