The first vials of Johnson & Johnson’s newly approved vaccine are expected to arrive in the Washington region this week, though they won’t be enough to reshape the enormous gulf between eligible residents and scarce appointments.

On Monday, Maryland Gov. Larry Hogan (R) said his state will receive 49,600 doses of the Johnson & Johnson vaccine, which represents a roughly 40 percent increase over the previous week’s total dose allotment. In Virginia, roughly 69,000 doses are expected to be distributed initially, primarily to mass vaccination sites. D.C. had not announced its allocation as of Monday evening.

Yet with millions of eligible people in the region competing for hundreds of thousands of available doses each week, experts say the distribution of a third vaccine won’t fundamentally fix the nationwide shortage just yet.

“It’s not going to narrow the gap between demand and supply, but it’s going to help,” said Jesse Goodman, director of Georgetown University’s Center on Medical Product Access, Safety and Stewardship and a former chief scientist at the Food and Drug Administration. But, he said, “we have to continue to fix the distribution and to get more vaccine to as many people as quickly as possible . . . We want to take advantage of having increasing supply of vaccines and not have it sit on the shelf.”

Maryland, in particular, has lingered in the bottom quarter of jurisdictions for administering doses that have been delivered to providers, according to an analysis of Centers for Disease Control and Prevention data by Becker’s Hospital Review. The state says its internal data shows it doing better but acknowledges that some providers have been slow to administer second doses.

As of Monday, Maryland had used 72.16 percent of the doses allocated to it, ranking 44th among all states. Virginia ranked 17th with 82.25 percent of its doses administered. A Washington Post analysis of CDC data showed D.C. with a rate similar to Maryland’s, with 69.6 percent of doses administered.

Among the many examples of demand far outstripping supply for the vaccine: Children’s National Hospital opened a wait list to give Pfizer doses to 16- and 17-year-olds in D.C. with qualifying health conditions who wanted the vaccine, but closed it after just a day, when all 200 slots quickly filled up. It’s the only place in the city where teenagers those ages with qualifying health conditions can sign up to get vaccinated.

Diana Troese, a spokeswoman for the hospital, said that Children’s National will reopen its wait list with 200 spots at a time, and new spots may open daily.

News that Johnson & Johnson vials were en route came the same day the Washington region surpassed 1 million confirmed coronavirus cases in the year since the pandemic began.

The influx of Johnson & Johnson doses, part of 3.9 million doses shipped nationwide starting over the weekend, might be short-lived, Hogan cautioned. He said in a news release that the company was shipping its entire inventory at once and that “future allocations of J&J could be uneven, and may be significantly smaller than this week’s allocation.”

Maryland spread out doses of the one-shot Johnson & Johnson vaccine among local health departments, hospitals and other providers in the state. About 55 percent of the Johnson & Johnson doses will go to two of the state’s four mass vaccination sites, M&T Bank Stadium in Baltimore and Regency Furniture Stadium in Charles County. The state urged providers to administer the doses to people who need to quickly complete their vaccination course.

Virginia officials are still working out the details about which clinics will receive the new one-dose vaccine, or the two-dose regimens made by Pfizer and Moderna.

The state’s allotment of Johnson & Johnson vaccine is expected to fluctuate at first, going down before it picks back up, said Dena Potter, a spokeswoman for the Virginia Department of Health.

Jenna Portnoy and Julie Zauzmer contributed to this report.