The last confirmed sighting of Mr Peters was at 11.55pm in Coney Street, York on Sunday 2 October 2016.
Officers are currently reviewing CCTV around the area in which he was last seen. An underwater search team is also due to search the River Foss today.
Mr Peters, who lives in the Hull Road area, is slim, 175cms tall and has dark brown hair. He was last seen wearing glasses, jeans or chinos, a black jacket and a navy blue polo shirt.
Inspector Martin Metcalfe, who is based in York, said:
Ethan has not been seen since Sunday and his disappearance is completely out of character.
We’re working closely with his family and providing support to them during this difficult time.
We’re also continuing to appeal for the public’s help are keeping an open mind with regards to the investigation.
I’d like to reiterate our appeal for information today – it’s vital that anyone who thinks they may have seen Ethan since Sunday or has any other information contacts us immediately on 101.
Please quote incident number 12160180683 when passing on information.