Do the prayers of one person affect the world?YES!We offer unto Thee, O Lord, the chalice of salvation, beseeching Thy clemency, that it may ascend in the sight of
Thy divine majesty with a sweet savour, for our own salvation and for that of the whole world. Amen
Taken from the Ordinary of the Mass after the Offertory. You are one person, and I am one person - each Catholic is one person.
It is the great power that Catholics alone (united in prayer as single persons) are given and authorised/obligated by Almighty God to pray for the whole world because they are baptised members of His One, Holy and Apostolic Church.
He died to save the souls of every single person because..
......he was the true light which enlighteneth every man who cometh into the world (Last Gospel)
It can be seen that through the Sacrament Catholics are obliged to pray for everyone. Whether or not everyone accepts the invitation is another matter left to God to judge.