In addition to touching and healing those who were afflicted in the Old World, Jesus was also petitioned to touch the little children:
Mark 10:13-16
13 ¶ And they brought young children to him, that he should touch them: and his disciples rebuked those that brought them.
14 But when Jesus saw it, he was much displeased, and said unto them, Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God.
15 Verily I say unto you, Whosoever shall not receive the kingdom of God as a little child, he shall not enter therein.
16 And he took them up in his arms, put his hands upon them, and blessed them.
The parents would bring the children to him perhaps as a preventative curing touch. Perhaps it was to simply bring them in contact with one so holy and powerful so that the spirit that obviously accompanied Jesus would beneficially effect the children. In the New World, Jesus initiates this ministry to the children, and asks that they be brought to him.