After all the nations of the earth have been conquered, or have subjected themselves to the rule and authority of Christ and the saints, the reign of Christ over the earth will begin and continue for 1000 years. Christ will reign over the mortal populations of the earth, ending war. We learn of this reign in Revelations:

REV 20:4-6 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years. But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection. Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.

During the 1000 year reign of Christ, sickness and death and all the results of Adam's sin on the earth will be greatly reduced. The general condition of the mortal population of the kingdom is described thus:

ISA 65:19-20 And I will rejoice in Jerusalem, and joy in my people: and the voice of weeping shall be no more heard in her, nor the voice of crying. There shall be no more thence an infant of days, nor an old man that hath not filled his days: for the child shall die an hundred years old; but the sinner being an hundred years old shall be accursed.

Therefore Christadelphians believe:

XXVI.--That the Kingdom of God thus constituted, will continue a thousand years, during which sin and death will continue among the earth's subject inhabitants, though in a much milder degree than now.