It is my understanding that after the destruction of the temple, those that were not removed fled to Egypt....Jerusalem was desolate. Nebuchadnezzar then advanced on Egypt and brought those Jews to Babylon.
2Kings 25:22-26 As for the people left behind in the land of Judah, whom Nebuchadnezzar the king of Babylon had left behind, he now appointed over them Gedaliah the son of Ahikam the son of Shaphan. When all the chiefs of the miliatry forces, they and their men, heard that the king of Babylon had appointed Gedaliah, they immediately came to Gedaliah at Mizpah, that is Ishmael the son of Nethaniah and Johaman the son of Kareah and Seraiah the son of Tanhumeth the Nethophathite and Jaazaniah the son of the Maacathite, they and their men. Then Gedaliah swore to them and their men and said to them: "Do not be afraid of [being] servants to the Chaldeans. Dwell in the land and serve the king of Babylon, and all wll go well with you." And it came about in the seventh month that Ishmael the son of Nethaniah the son of Elishama of th royal offspring came, and also ten men with him, and they got to strike down Gedaliah, so that he died, and also the Jews and Chaldeans that happened to be with him in Mizpah. After that all the people, from small to great, and the chiefs of the military forces rose up and came to Egypt; for they had beome afraid of the Chaldeans.
As for Josephus, his writings confirm both the servitude and the desolation of 70 years:
Antiquites of the Jews X, Chapter 7, Paragraph 3 But Jeremiah came among them, and prophsied what contradicted those predictions, and what proved to be true, that they did ill, and deluded the king; that the Eqyptians would be of no advantage to them, but that the king of Babylon would renew the war against Jerusalem, and besiege it again, an would destroy the people by famine, and carry away those that remained into captivity, and would take away what they had as spoils and would carry off those riches that were in the temple; nay, that, besides this, he would burn it, and utterly overthrow the city, and that they should serve him and his posterity seventy years; that then the Perians and the Medes should put an end to their servitude, and overthrow the Babylonians;"'and that we shall be dismissed, and returned to this land, and rebuild the temple, and restore Jerusalem"
Jeremiah 25:12 And it must occur that when seventy years have been fulfilled I shall call to account the king of Babylon and against that nation, is the utterance of Jehovah, their error, even against the land of the Chaldeans, and I will make it desolate wastes to time indefinite.
With the fall of the Babylonian empire in 539 BCE the 70 years of servitude to Babylon has been completed.
Jeremiah 27:6-7 And now I myself have given all these lands into the hand of Nubuchadnezzar the king of Babylon, my servant, and even the wild beasts of the field I have given him to serve him. And all the nations must serve even him and his son and his grandson until the time even of his own land comes, and many nation and great kings must exploit him as a servant.
Nabonidus is Nebuchdnezzar's son-in-law, Belshazzar his grandson.
Antiquities of the Jews X, Chapter 9, Paragraph 7 ....placed no other nation in their country, by which means all Judea and Jerusalem, and the temple, continued to be a desert for seventy years; but the entire interval of time which passed from captivity of the Israelites, to the carrying away of the two tribes, proved to be a hundred thirty years, six months.....
716 Israel falls to the Assyrians, 586 Temple is destroyed. The interval is 130 years.
Against Apion #19...Nabolassar, who was king of Babylon, and of the Chaldeans. And when he was relating the act of this king, he describes to us how he set hi son Nabuchodonosor againt Egypt,and against our land, wih a great army, upon his being informed that they had revolted from him; and how, by that means, he subdued them all, and set our temple that was at Jerusalem on fire; nay, and removed our people entirely out of their own country, and transferred them to Babylon; when it so happened that our city was desolate during the interval of seventy years, until the days of Cyrus king of Persia.
The temple destruction in 586 BCE is confirmed above. Cyrus released the Jews in 537 BCE. At this point Jerusalem had been desolate for 50 years.
Against Apion #21 These accounts agree with the true hitories in or boks; fo in tm it is written that Nebuchadnezzar, i the eighteenth year of his reig, laid our temple desolate, and so it lay in that state of obscurity for fifty years; but that in the second year of the reign of Cyrus its foundations were laid, and it was finshed in the second year of Darius.
In Darius' second year, 520 BCE, temple reconstruction was resumed and finished in the 6th year of his reign 516 BCE. This ended the 70 years of devastation for Jerusalem
Ante-Nicene Fathers, Ireneus Against Heresies, BookIV, Paragraph 4 If any one, however, advocating the cause of the Jews, do maintain that this new covenant consisted in the rearing of the temple which was built under Zerubbabel after the emigration to Babylon, and in the departure of the people from thence after the lapse of seventy years, let him know that the temple constructed of stone was indeed rebuilt....
Daniel 9:2 In the first year of his reigning I myself, Daniel, discerned by the books the number of years concerning which the word of Jehovah had occurrd to Jeremiah the prophet, for fulfilling the devastations of Jerusam, [namely] seventy years.
The first year of Darius was 521 BCE. Daniel had never returned to Jerusalem
The temple was completed in the 6th year of Darius, 516 BCE. The period of devastation confirmed with Josephus was 586 BCE - 516 BCE
Excuse any typos. My keyboard is freezing on me.....time to reboot
AddaGirl