The Daniel 8:13 phrase,
"... to give both the sanctuary and the host to be trodden under foot," aligns with the Revelation 11:1-2 events in Jerusalem at the end involving the future 3rd temple to be built by the Jews, as they will be the ones that worship inside it.
Rev 11:1-2
11 And there was given me a reed like unto a rod: and the angel stood, saying, "Rise, and measure the temple of God, and the altar, and them that worship therein.
2 But the court which is without the temple leave out, and measure it not; for it is given unto the Gentiles: and the holy city shall they tread under foot forty and two months."
KJV
That 42 months the Gentiles will be given to
"tread under foot" is equal to the latter 1260 days half of the Daniel 9:27 symbolic
"one week". Per Rev.13:4-8, that 42 months also represents the time the "
dragon" (Satan) will be given to reign over all nations and over the saints, at the very end of this world. Thus that Dan.8:13 phrase is another connection to events for the END of this world, and thus shows again the Daniel 9:27 events are for the END also, and were not past history.
The "abomination that maketh desolate":
Per Daniel 11:21, a
"vile person" is to appear in Jerusalem and make a "
league" with a small group of Jews there, which is what the Dan.9:27
"confirm the covenant" will be about for the end. What that will be about is the re-establishing of a future 3rd temple to be built by the Orthodox Jews in today's Jerusalem, and their starting up the old covenant worship again in Jerusalem. (the Jews in Jerusalem already have the materials ready to start building it, and have been training Levite priests for the temple service).
That
"vile person" will be the final Antichrist at the end of this world. He will take the kingdom in Jerusalem,
"... he shall come in peaceably, and obtain the kingdom by flatteries." (Dan.11:21) After his power is stirred up, per Dan.11:28, when he returns to his own land,
"... his heart shall be against the holy covenant: ...". Because mention of the
"holy covenant" is given there, it shows the old covenant worship by the orthodox Jews in Jerusalem will be re-established for the END. Per Dan.11:30, that "
vile person" will
"... have indignation against the holy covenant: so shall he do; he shall even return, and have intelligence with them that forsake the holy covenant."
At that point is when that "
vile person" (Antichrist) will end... the Jew's future daily sacrifices and old covenant worship with their 3rd temple. The "
vile person" will instead have an IDOL abomination placed inside the temple for worship instead, which is what the "
abomination" below is about, and aligns with the "
image of the beast" IDOL that will be setup at the END of this world per the end of Revelation 13...
Dan 11:31
31 And arms shall stand on his part, and they shall pollute the sanctuary of strength, and shall take away the daily sacrifice, and they shall place the abomination that maketh desolate.
KJV
It is the above verse from the Book of Daniel 11:31 that Lord Jesus quoted as warning in His Olivet discourse SIGNS for the END of this world...
Matt 24:15-21
15 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand
16 Then let them which be in Judaea flee into the mountains:
17 Let him which is on the housetop not come down to take any thing out of his house:
18 Neither let him which is in the field return back to take his clothes.
19 And woe unto them that are with child, and to them that give suck in those days!
20 But pray ye that your flight be not in the winter, neither on the sabbath day:
21 For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be.
KJV