The family of a British hiker missing in New Zealand’s Mount Aspiring national park say they are “hoping upon hope” that she will be found more than five days after she went missing in rugged bushland.

Stephanie Simpson, 32, has not been seen since she went for a hike at the weekend in the national park, home to one of New Zealand’s highest peaks.

Police started looking for Simpson after she failed to keep an appointment on Monday and was reported missing.

More than a dozen people and two dog teams have resumed the search in the South Island park, with thermal imaging technology, drones and a helicopter also being deployed.

The search is focusing on the area from Fantail Falls to Mount Brewster, police said, as well the Brewster Hut and Mount Armstrong track, and also Makarora Valley.

“It is a large search area and much of it is difficult terrain,” police said in a statement.

Simpson’s family, who live in Essex, said they were becoming desperate for news.

Her brother-in-law, Sam Hazelton, told the New Zealand Herald that the worst thing was not knowing what had happened. The family were at “their wits’ end”, and were just doing their best to cope day-to-day.

“You can’t imagine, it’s pretty awful.” Hazelton said. “Everybody’s just hoping. You go to bed thinking: ‘What can we do?’

“And then you wake up, or keep checking your phone to get an update ... the hard thing is the delay and then nothing comes.”

Hazelton praised the efforts of New Zealand police and said they were doing everything possible to locate Simpson.

According to the New Zealand Mountain Safety Council, 57 hikers, or trampers as they are called in New Zealand, died in the 10 years to June 2017, with international tourists making up close to half.

Last year, 600,000 international visitors went hiking in New Zealand, a 34% rise on 2014. There has been an 83% increase in related injuries over the past 10 years, with an average of 4,000 injuries a year.

More than 500 search and rescue operations for lost hikers are carried out every year.