The 37-year-old was last seen leaving South Tyneside District Hospital in South Shields at 8am on Saturday, February 27, before he was given treatment for what is thought to be a serious injury to his stomach.
Northumbria Police has said the force is growing increasingly concerned for his welfare and have issued an appeal for help to find him.
Yesterday, Monday, March 1, it confirmed it was carrying out a search of Temple Memorial Park, which is just a short distance away from the hospital, with inquiries continuing into today to try and locate him.
As part of the effort Northumberland National Park Mountain Rescue Team and North of Tyne Mountain Rescue Team were called to the park at 1.10pm and spent almost five hours carrying out a sweep of the land.
Earlier today, a spokesperson for the Northumberland team, which sent 10 of its members, said: “Northumbria Police requested Mountain Rescue’s assistance for a missing person search in South Shields yesterday afternoon.
"The missing person had last been seen on two days earlier and the police were increasingly concerned for their wellbeing.
"In discussion with the Police Search Adviser it was agreed that North of Tyne Mountain Rescue Team and ourselves would deploy.
"Team members worked alongside police officers to search Temple Memorial Park.
"Despite our collective efforts nothing was found and police inquiries are ongoing.”
The search and rescue teams are led by volunteers and funded through donations.
Police have described Mr Thompson as around 6ft tall, of slim build and bald and was last seen wearing a blue hat, black face mask with a grey hooded top, a navy jacket and black tracksuit bottoms with white trainers.
CCTV images have been released as part of the search showing what he was wearing at the time of his disappearance.
He or anyone with information about his whereabouts, is asked to get in touch immediately by calling 101 and quoting log number 275 27/02/21 or use the Tell us Something page of the force’s website.