Three weeks of sheltering in place have noticeably lessened the impact of the coronavirus in the Bay Area, where the number of new infections is already slowing down even as federal officials warn that other parts of the country may be facing their worst weeks.

In other words: That dreaded curve is starting to flatten out, just a little.

Case counts are still climbing across the Bay Area, where nearly 3,800 people have tested positive for the COVID-19 virus. But they’re climbing much less rapidly than they were even a week ago.

In San Francisco, the Public Health Department reported slightly fewer new cases last week than the week before, and though that may be explained by fluctuations in testing and reporting, it’s still a startling change from the constant upward trend of the past month.

“At this stage, it looks like the beginnings of a trend toward flattening. It’s unmistakable for some counties,” said Travis Porco, a biostatistician at UCSF who has been tracking several data points to follow the progress of the Bay Area outbreak. “I definitely am guardedly optimistic.”

The pandemic is exploding across the United States, which has reported nearly 370,000 cases — more than twice as many as any other country. More than 10,000 people have died of COVID-19 in the U.S.

And over the weekend President Trump and other national leaders braced the country for a tough week ahead as parts of the United States — including New York, New Jersey, Michigan and Louisiana — confronted explosive outbreaks that in some places already are overwhelming health care systems.

Though the Bay Area may be showing signs of faring much better than the rest of the country, there are still pockets of concern, including alarming outbreaks at Laguna Honda nursing home and a residential care facility in Orinda. San Francisco and Santa Clara counties together have reported 16 cases among homeless people, including two in the region’s largest shelter, which has public health officials worried about the potential for more widespread illness among a particularly vulnerable population.

Now Playing:

Dr. Susan Philip, director of disease prevention and control at the San Francisco Department of Public Health, said Monday that though she’s heartened to see hints that the outbreak is weakening, she expects case counts to continue to climb as testing ramps up.

“While we’ll always take a little good news, it’s too early to say we’re out of the woods,” Philip said. “We don’t want people to feel like it’s time to let up. We’re still concerned with a surge, and not wanting to see a large number of people becoming sick all at the same time.”

State and local leaders have warned that even with social distancing practices in place, California can expect to see a rising tide in people needing hospital care over the next few weeks. The state is expected to hit the peak of its outbreak sometime in May.

That’s later than other parts of the country because the state so far is successfully thinning out the number of people infected. Even with shelter-in-place orders in effect, some people will continue to get sick — from hospitals and other health care settings, for example, or from going out into the community, even if they’re taking precautions — but those numbers will, hopefully, remain manageable for the state’s health care structure.

“Every week that goes by, when we look at the numbers we brace ourselves,” said Dr. Jahan Fahimi, an emergency physician at UCSF Medical Center. “And every week, while we’re taking care of COVID-positive patients, it’s not overwhelming. We have the bandwidth to manage them.

“There are days when it feels to me like the surge has not come and maybe we’re through this, maybe we’re near the peak of the curve,” he said. “But I don’t think we’re going to know where the peak is until we’re past it. Very smart people still are anticipating the surge to come.”

Infectious disease experts also are gaining confidence that the region may emerge from its outbreak with far less damage than they once feared, likely due in large part to early and aggressive efforts to encourage physical distancing. Six Bay Area counties were the first in the country to order residents to shelter in place, three weeks ago.

UC Berkeley infectious disease expert Art Reingold said he’s “optimistic” that the Bay Area will be able to avoid a devastating surge in local hospitals if residents can keep observing stay-home orders.

“The hope is that these early and strong efforts by various counties are bearing fruit,” Reingold said, “and that we will not have anything like the kind of upward trajectory in the coming weeks that other cities in the United States seem to experience.”

In the Bay Area, last week was the first since the outbreak took off in early March that the region did not see new cases double over the previous week, according to a Chronicle analysis. There were 1,666 new cases reported March 29 to April 4, which was about a 50% increase over the previous week.

The trend holds up across the individual Bay Area counties. San Francisco stands out as the only large county to see the number of new cases drop, though by only three: 221 last week compared to 224 the week before. Santa Clara County, which has been driving the regional outbreak, reported 557 new cases last week — a 70% increase, but still an improvement from the week-over-week doubling.

Case counts are an imperfect way of tracking trends in the pandemic, in part because not nearly enough people have been tested, and who gets tested varies from week to week. Testing has increased in recent weeks, and Porco said he and other statisticians are trying to tease out what effect that’s having on county case reports.

Now Playing:

But the fact that case counts aren’t increasing as rapidly as they were even two weeks ago is encouraging given that testing has also increased in that time, Porco said.

“You do see a flattening of the curve, and even a noticeable turn down in new cases per day,” he said. “I’d like to see good, sustained evidence of that now.”

Aside from case counts, there are other signs of movement in the right direction for the Bay Area, infectious disease experts said. Several counties have recently started reporting the number of people hospitalized with COVID-19 each day, and though they’ve been climbing, they’re not moving fast.

Statewide, Gov. Gavin Newsom said Monday that 2,509 people are hospitalized, of which 1,085 are in intensive care — both of those numbers were up about 5% from the day before. About 450 people are hospitalized in the Bay Area, according to the California Department of Public Health, though the numbers it reports are somewhat lower than individual county reports.

More than 16,000 people have tested positive for COVID-19 in California, and 385 people have died.

“We cannot allow cabin fever to come in. We cannot allow people to start congregating again,” Newsom said. “Let’s hold the line; let’s keep doing the good work we’ve done so far. Keep those numbers below those worst-case projections.”

Erin Allday is a San Francisco Chronicle staff writer. Email: eallday@sfchronicle.com