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Prince George’s County closed coronavirus vaccination appointments to nonresidents on Monday, and Inova Health System canceled thousands of appointments for Fairfax County teachers as providers across the Washington region scrambled to compensate for a limited supply of vaccine doses.

Prince George’s halted vaccination appointments for nonresidents who were eager to get the shot wherever it was available. County Executive Angela D. Alsobrooks (D) said the county canceled the appointments after hearing from residents who were unable to secure a time slot amid growing competition for doses.

The situation underscored the difficulty that localities and health departments face in balancing the ballooning eligibility pools while not having enough vaccine to go around. Local governments began the week pleading for more doses to meet the demand.

Inova late Monday said it canceled scheduled vaccinations for teachers and staff members in Fairfax County Public Schools “for the foreseeable future.” The decision affects at least 15,000 school district employees — roughly 60 percent of its workforce — all of whom registered for doses under the 1B phase of Virginia’s vaccine rollout.

Inova, which has been administering the Fairfax school district vaccinations, said in an email to school staff members that a national vaccine shortage prompted the Virginia Department of Health to direct vaccine doses away from hospitals, leaving its supply “severely diminished.”

“We understand and share the frustration that this news brings to our patients,” the letter said. “We are working diligently to identify new supply.”

The roughly 7,000 Fairfax schools employees who already received their first shot of the two-dose regimen will still receive their second vaccination, officials said.

Virginia Hospital Center in Arlington on Friday canceled 10,000 vaccination appointments, citing the same change in the state’s allocation system. Arlington will reschedule those, but appointments for second doses will not change, the hospital said in a statement.

D.C. Mayor Muriel E. Bowser (D) on Monday received her first dose of vaccine as part of a broader push to bolster public trust in its efficacy. The District will receive 14,376 doses this week, but the city’s health director, LaQuandra Nesbitt — who wore a mask Monday that read “DC needs more vaccine” — said doses remain in short supply.

Maryland officials said Monday that the state opened eligibility to three times as many people as the current supply could accommodate as part of a strategy to quickly administer doses. Montgomery County began allowing residents 75 and older to register for vaccination appointments on Monday, said Health Officer Travis Gayles, while officials also petitioned Gov. Larry Hogan (R) for more doses from the state.

As more people slowly get vaccinated, infection rates have continued to hover at elevated levels.

The first case of the virus variant found in Britain was discovered in a Northern Virginia resident who has not recently traveled, the state announced Monday. The development came days after Maryland confirmed its first two cases of the variant, which officials say is more contagious but not necessarily more deadly than the original virus.

The Virginia Department of Health declined to say where the newly infected person lives or release details about the case.

In Prince George’s, Alsobrooks said Monday that health officials decided to cancel appointments after hearing from county residents in priority groups 1A and 1B who were unable to get appointments and then seeing how many appointments had been filled by nonresidents.

“We share those concerns,” she said at a news conference. “I apologize. . . . We had to ensure that equity occurred in terms of the delivery of the vaccine in our community.”

Alsobrooks said canceled appointments are being filled by seniors who live in the county who have preregistered and others who work in the county and fall into the 1A and 1B categories. She said that she understood there would be disappointment from those with canceled appointments but that the priority of health officials must be county residents.

Those who received their first dose of the vaccine in the county will be able to receive their second dose, Alsobrooks said, even if they are not residents. Under the new guidelines, people must bring proof of residency or information that shows they work in Prince George’s to make their inoculation appointment.

Alsobrooks encouraged residents who fall into the 1C category — which includes those 65 and older — to fill out registration paperwork, but she said it could be weeks before they begin receiving vaccinations.

Alsobrooks also announced Monday that indoor dining will be allowed to resume beginning Friday, at 25 percent capacity. She said health officials decided to end the ban because of improved metrics, including a positivity rate below 10 percent.

In Montgomery County, people 75 and older who filled out the county’s preregistration form should expect to receive an email from the county this week inviting them to set up an appointment, Gayles said. Teachers, child-care providers and other groups under the state’s 1B categorization still have to wait, he said.

“We respect that other counties are moving quicker at their own pace, [but] we’re moving as fast as we can with the doses we’ve received,” Gayles said.

The county government has received 31,200 vaccine doses, which is not enough to cover the 60,000 people in group 1A, much less the 75,000 others in group 1B, officials have said. Those allocations do not include what has been given to the county’s hospitals and nursing homes.

In a news conference Monday, county lawmakers called on the Hogan administration to provide more vaccine doses to Montgomery, the state’s most populous jurisdiction.

Council President Tom Hucker (D-District 5) said state officials caused confusion and panic among Montgomery residents by announcing that the state would expand eligibility to priority group 1C this week. “We just don’t have the doses to do that,” he said of the county.

Frederick County also announced Monday that it would not yet broaden access to the vaccine, saying it is still focused on inoculating health-care workers and people 75 and older.

The decisions at the local level leave scores of people otherwise eligible to receive the vaccine unable to make appointments, including some people in priority groups 1B and all of 1C — a population that covers teachers, child-care workers and people ages 65 to 74.

Top Maryland officials acknowledged Monday that people such as teachers will have to “compete” with seniors for limited vaccine appointments.

“It’s going to be very competitive,” acting health secretary Dennis Schrader told a panel of state senators.

Schrader said his personal preference would have been to let more people in group 1B, which includes people 75 or older and teachers, to get vaccinated before expanding eligibility further. But, he said, “the federal government forced our hand a little bit. . . . They insisted that [people aged] 65 and older should be put in the mix.”

Schrader said the imbalance between demand from eligible residents and insufficient supply is likely to make it difficult to obtain appointments for weeks.

Maryland has received 667,275 doses, but, as of Monday, roughly 2.1 million people are eligible to get a shot. Statewide, 330,709 first doses have been administered, and 42,228 people are fully vaccinated.

In Virginia, 458,472 first doses have been administered, and 64,381 people are fully vaccinated. The state has distributed about 1.1 million doses.

Of the 68,750 vaccine doses distributed in the District, 51,421 have been administered.

The District will receive 8,776 additional doses of the Pfizer vaccine and 5,600 doses of the Moderna vaccine this week, Bowser and Nesbitt said during a news conference.

The city is in its Phase 1B Tier 2 group, which includes teachers and some essential workers. Nesbitt said the city needs more vaccine doses to reach everyone in the group, calling the city’s current allocation “dismal.”

“I’d appreciate an amplification of this message, which is that we simply do not have enough vaccine,” she said.

D.C. public school teachers will begin receiving vaccinations this week, Bowser said, and about 70 percent of the 3,900 slots for those teachers have been filled. The city’s Fire and EMS workers and D.C. police began receiving vaccinations, while seniors and health-care workers can continue to register. Nesbitt said the latest group includes officials in the “succession plan for government” — a group of 50 government employees that includes the mayor.

Bowser, who said she hates needles, made a point to say the vaccine was safe and implored residents to remind their friends and family who are 65 and older they are eligible to receive it.

Bowser sat with her eyes closed as a nurse administered her first dose of the Pfizer vaccine at Kaiser Permanente Capitol Hill Medical Center. Afterward, the mayor raised her arm in triumph, and relief.

“That wasn’t bad at all,” she said with a laugh.

Michael Brice-Saddler and Erin Cox contributed to this report.