You are very close to the truth, except for the fact that today's Jews are more closely related to the Khazars (Asiatic people) than they are to biblical Israel. The Khazars converted to Judaism, en masse, in the 7th & 8th Centuries, A.D. They are “Jews” by religion and by name, but not by blood (save the few incidents where they may have married peoples with Israelite blood).
Revelation 2:9, “I know thy works, and tribulation, and poverty, (but thou art rich) and I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan.”
Revelation 3:9, “Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.”
The Bible also reveals in the books of Ezra and Nehemiah that when the men and women of Judah (sometimes referred to as Jews) were permitted to return to Jerusalem to rebuild that city, that they returned as a “mixed multitude.” That is to say that they had married into the non-Israelite peoples of the region (Canaanites, Edomites, etc.). Ezra and Nehemiah were NOT happy, had many harsh things to say about it.
There is so, so, so much more to be said about the actual history of the 10 northern tribes of Israel (the “lost tribes of Israel”) and the 2 southern tribes of Israel (Judah & Benjamin). But if there's anything I've learned about discussion forums is that people believe what they believe and no amount of facts will change their beliefs, so I rarely waste my time and energy anymore.
Anyway, modern Israel isn't found in the Middle East.