LOS ANGELES — Skittish even at the best of times, homeless people in Orange County have been running to shelters this week in search of a safe place to sleep after the separate stabbing deaths of three homeless men. The authorities believe there is a serial killer stalking the homeless.

Demand for beds at some shelters was up as much as 40 percent in the last couple of days, while other shelters have been inundated with calls from frightened homeless people wondering if the killer has been caught, whom he is targeting and where they can go.

Jim Palmer, president of the Orange County Rescue Mission, said the prospect of a serial killer in their midst had shaken the county’s homeless like nothing he had seen in the last two decades.

“People are very, very anxious about the situation,” Mr. Palmer said. “This is just so evil that somebody would go after the least, the last and the lost of our community: homeless people on their own.”