As containment efforts falter, the measles outbreak in West Texas is likely to persist for a year, perhaps even setting back the country’s hard-fought victory over the virus, according to Texas health officials.

As of Friday, the outbreak had sickened more than 300 people in Texas since January; 40 have been hospitalized. One child has died from the disease, the first such death in a decade. Related cases have been reported in New Mexico, Oklahoma and Chihuahua, Mexico.

“This is going to be a large outbreak,” Katherine Wells, director of public health in Lubbock, Texas, said at a recent news briefing. “And we are still on the side where we are increasing the number of cases.”

“I’m really thinking this is going to be a year long,” she added.

Some doctors in West Texas said in interviews that they had given up hope that a vaccination campaign could end the outbreak.

Dr. Ron Cook, also a state health official in Lubbock, said he had resigned himself to the fact that the outbreak will infect many more children, and may kill again.

“It’s just going to have to burn through the community,” Dr. Cook said. “That’s where we are.”

So far, cases have been centered in a large Mennonite community in Gaines County, which has had historically low vaccination rates. But experts fear that the longer the outbreak lasts, the more likely it is to spread to other unvaccinated communities around the country.

In New Mexico, officials have reported 42 cases and one death. In Oklahoma, there have been four probable measles cases.

Public health officials are particularly concerned now that potentially infected children in West Texas will begin traveling for spring break, said Dr. Phil Huang, director of Dallas County Health and Human Services.

Measles has been considered “eliminated” in the United States since 2000: Cases generally have been tied to international travel, and when the virus does strike an unvaccinated community, the outbreaks don’t continue for longer than a year.

The United States nearly lost its elimination status in 2019, when a large outbreak spread through parts of New York State for nearly 12 months. The outbreak was contained in large part because of aggressive vaccine mandates, which helped substantially increase childhood immunization rates in the community.

In Texas, where mandates are deeply unpopular, the vaccination effort has “been a struggle,” Ms. Wells said. Public health officials have set up vaccination clinics around the region and encouraged attendance with fliers and billboards. There has been little success.

In Seminole, Texas, a city of about 7,200 people and the epicenter of the outbreak, roughly 230 residents have received shots at vaccination clinics.

“They’ve handed out a few vaccines in their community, but certainly not a lot,” Dr. Cook said.

“It doesn’t help that our H.H.S. secretary continues to not really reinforce vaccination,” he added.

Local efforts to encourage the shots have been hamstrung by a muddled message from the country’s top health official, Robert F. Kennedy Jr.

In his first public statements about the outbreak, Mr. Kennedy faced intense backlash for minimizing the threat, saying outbreaks were “not unusual” and falsely claiming that many people hospitalized were there “mainly for quarantine.”

He later changed his approach, offering a muted recommendation of vaccines for people in West Texas while also raising frightening concerns about the safety of the vaccines.

To the frustration of local doctors and health officials, he has also promoted unproven treatments like cod liver oil and vitamins, and touted “almost miraculous and instantaneous” recoveries with steroids or antibiotics.

There is no cure for measles, only medications to help manage the symptoms. Vaccination is the most effective way to prevent the infection.

Texas health officials have said they worry that measles patients were over-relying on these unproven treatments and delaying critical medical care as a result.