On the Kenai, a struggling family or a teenager can escape notice against the vast landscape.

“Homelessness is a hidden problem,” said Steve Atwater, the superintendent of the Kenai Peninsula school district, where about one in 90 students are enrolled this year in a program to keep them in school, even if they have no permanent address. That number is down slightly from last year, and district officials suspect that the main reason is an unseasonably warm fall.

From 2011 to 2012, Alaska’s overall homeless rate declined 10 percent, according to a report this year by the National Alliance to End Homelessness, a federation of organizations. But the number of chronically homeless people rose almost 21 percent, giving Alaska the ninth-highest increase in the nation.

Couch surfers, crashing with friends, often do not consider themselves homeless. And in a state where camping is both a way of life and part of the heritage, living in a tent in the woods might be by choice, or it might not be.

“We kind of called it camping,” said Tammy Miles, who lived in the woods in a tent for 132 days this summer — a number she repeated twice more with grim, tight-lipped finality — with her two autistic sons, ages 10 and 7, after her boyfriend of 13 years left her stranded and then homeless. She and the boys were in a family shelter — the only one in Kenai Borough, a county bigger than West Virginia — when it closed in June because of financial troubles, sending them into the wild. It was the family’s second eviction in a year.

On a recent afternoon, with the temperature topping out at about 6 degrees, a campsite just outside downtown looked ghostly in the frost. The occupants were gone, presumably indoors. A spatula and a can of pepper sat on a folding table by a small camp stove, ready for use. Were the campers there by choice, or were they homeless? On Kenai Peninsula, it can be hard to tell.

There is a sense that hunger, a more easily measured barometer of stress, is increasing. At the Kenai Peninsula Food Bank in the nearby town of Kenai, the number of people seeking free commodities like canned goods and rice is higher than at any time since 2010, when the recession was at its worst. A trend toward younger people and families coming in hungry has persisted, said Linda Swarner, the food bank’s executive director.