The heartbroken family of a four-year-old who disappeared from a remote homestead in the South Australian outback four days ago is holding onto hope he will be found alive.

He was reportedly playing in his grandparents’ sandpit around the time he went missing.

Friend of the family Bill Harbison read out a statement today on their behalf.

In it, Gus’ loved ones said they were still desperately hoping the four-year-old will be found alive three nights and four days after he went missing.

“We are devastated by the disappearance of our beloved Gus on Saturday afternoon,” the statement reads.

“This has come as a shock to our family and friends, and we are struggling to comprehend what has happened.

“Gus’ absence is felt in all of us, and we miss him more than words can express. Our hearts are aching, and we are holding onto hope that he will be found and returned to us safely.”

The statement added: “We are incredibly grateful to the South Australia Police, emergency services and the many organisations and community members, neighbours and friends who have come together to help find Gus.”

The family said they are “deeply distressed” and asked for privacy.

Superintendent Mark Syrus told reporters today that police were “throwing everything” at the search for Gus.

“Probably the biggest thing is the vastness of it. It’s such a big area and the frustrating thing for us is we actually haven’t got a direction of travel,” Syrus said.

“The more ground we cover the more chance we find something we might have discarded like a hat or a shirt or a boot and that’s, once we find that it gives us a bit more hope.

“The human body’s an amazing thing. We’re hoping that he’s just stayed put, kept out of the sun and last night was milder weather.”

It is believed to have gotten down to six degrees in the first two nights he has been missing.

SA Police Commissioner Grant Stevens said the “favourable” weather had given police hope that Gus could be alive.

“The weather conditions have been favourable which is something we’re pinning our hopes on,” Stevens said.

“Our intention at the moment is to continue searching until we find Gus. So we’re hopeful that that is sooner than later.

“It is proving to be challenging and there are lots of places where a small child might find themselves which would be hard for us to identify as easily as people may think.”

Stevens said police do not believe Gus was taken.

“We’re not following that line of inquiry at this stage,” he added.

Local officers searched the area with a helicopter and an infra-red camera the night Gus went missing, but were unable to find him.

Crews have also used trail bikes, ATVs, horses and a drone and a helicopter to scour a 2.5km radius from where Gus was last seen.

Yesterday, police attached to water operations searched dams and tanks on the property while officers on horses searched the property.

Gus was wearing a grey sun hat, a cobalt blue t-shirt with a yellow minion from the movie Despicable Me on the front, light grey long pants and boots.

His family have declined to release an image of him.