“Maggie” gives the familiar zombie apocalypse scenario a new twist. A grim, contemplative film starring Arnold Schwarzenegger in his first indie horror film, “Maggie” personalizes zombies.

The New Orleans area-shot film’s intimate storytelling dials down the volume, speed and massive numbers of walking and sometimes running dead usually seen in zombie movies and TV series.

Timing is key. Unlike the great British zombie movie from 2003, “28 Days Later,” the turn from human to zombie in “Maggie” doesn’t happen within seconds or minutes. It’s more like days and weeks.

That difference opens up storytelling possibilities within family and community dynamics. Zombies-to-be are family, friends and neighbors. Should a family have an infected person in their home, authorities monitor the afflicted and, before the turn, carry them away to a horrible, officially sanctioned fate.

“Maggie,” like the 2009 film adaptation of Cormac McCarthy’s apocalypse drama, “The Road,” has a quiet, bleak end-of-days tone. Also like “The Road,” it’s a story about a father’s fierce will to protect his child by whatever means necessary.

Schwarzenegger stars as the farmer father of 16-year-old Maggie. She’s been bitten and has the incurable necro-ambulist virus.

Abigail Breslin co-stars as Maggie. After being diagnosed with the virus, Maggie runs away from home.

The film opens effectively. Schwarzenegger listens to a phone message from his daughter.

“Dad,” she says. “I’ve gone to the city. Please don’t come for me. There’s a curfew here. … I’m sorry. I love you.”

The loving dad Schwarzenegger plays, Wade Vogel, will have none of that. He drives his old pickup into the city and retrieves his daughter from a clinic for the infected. He’s taking his little girl home — at least for a while.

A low-budget movie set in the near future that appears to have no special effects, “Maggie” features only a handful of characters and locations. Most of the story takes place in or near Wade and his family’s isolated farmhouse. Just a few neighbors plus the local sheriff and his aggressive deputy come by for a visit.

The rural setting is conducive to Schwarzenegger’s brooding and his wife’s worrying. Joely Richardson co-stars as Caroline, Maggie’s stepmother. It’s especially difficult for Caroline to act naturally when her stepdaughter won’t even keep her bandages on that unsightly zombie bite. Schwarzenegger’s performance is, despite the great emotion his character is apparently feeling, minimal.

A series of banal scenes on the farm are regularly jolted by disturbing sequences, sparked by Maggie’s reaction to the zombie virus and its unstoppable progression.

First-time feature film director Henry Hobson — a graphic designer and commercial and title sequence director — makes the most of Maggie’s mad scenes. They are nightmarish. But scenes between Maggie’s freak-outs are lengthy dry spells. That makes “Maggie” less consistently interesting than it might have been.

“Maggie” also marks the feature film debut of its screenwriter, John Scott 3. A film that succeeds in spurts, “Maggie” most of all suggests that its director and writer are just beginning.