Because of Alzheimer’s disease, Edward Birkner thinks his wife, Elizabeth, is his sister, or maybe the maid. Birkner struggles to finish sentences. But he still has his moments.

Last October, Birkner, 83, wandered from his beachfront condo in Madeira Beach, Fla., with $9 and an American Express card in his pocket. He somehow managed to get to Tampa International Airport, where he bought a cheap ticket to New York City, pretty much making a beeline toward his summer home just north of the city.

At LaGuardia Airport, his odyssey took a detour. Maybe he gave jumbled directions to a cabbie. Maybe a willing stranger gave him ride, then got fed up with his confusion.

In any event, he ended up on the shoulder of the Connecticut Turnpike, 1,200 miles from home, shivering in his short-sleeves.

Birkner’s journey — aside from its resourceful cross-country scope — typifies a common yearning among people with serious dementia. They want to “go home,” even though they’re already home. They fixate on a destination, but have no idea where it really is.

What saved Birkner was a thin silver ID bracelet wrapped around his left wrist, courtesy of the Safe Return program run by the Alzheimer’s Association.

The bracelet listed a 24-hour hot line. Association computers immediately identified Birkner, where he lived, what medications he needed and whom to contact if he got lost.

Within hours, his son from Massachusetts drove to Connecticut and picked him up.

Sixty percent of people with dementia eventually wander, says Gloria Smith, director of the association’s Florida Gulf Coast Chapter. “They can be miles away in a matter of minutes. These folks can really cook.”

Other identification programs may list a wanderer’s name and address, which can work if home is nearby and the caregiver is available. The Safe Return bracelet works anywhere in the country.

Since it began 10 years ago, the Safe Return program has enrolled 100,000 people. About 8,000 have wandered far enough for strangers to call in and report them lost.

The program costs a one-time fee of $40, which includes the bracelet, ID tags for clothing and advice on modifying homes to reduce wandering.

Glitzier, more expensive prevention systems also have hit the market, including motion sensors for doors and windows, electronic alarms and a watch-like wrist band that emits a radio signal, traceable up to a mile away by someone carrying a receiving antenna.

Those who can afford it can even track down their loved ones with satellites. GPS systems can be strapped on a wanderer’s wrist. It looks like watch and can pinpoint a person’s location down to a few yards. The one-time cost is about $400, plus a monthly service charge between $25 and $35.