Sounding his most optimistic tone since the coronavirus crisis enveloped California, Gov. Gavin Newsom on Tuesday said the latest numbers and projections point to a compelling conclusion: Sheltering in place is making a difference, and we must keep it up.

The number of COVID-19 hospitalizations increased by just 4% Tuesday to 2,611, and the number of ICU beds in use increased by 2% to 1,108 — a far cry from the double-digit jumps the state was seeing a week ago, Newsom said.

Newsom said that as California’s curve starts to bend, it is also stretching, pushing the state’s peak back to late May. But those projections are at odds with some other recent estimates that the state could hit its peak in hospitalizations and deaths over the next week and a half, underscoring that even the state’s success to date has not clarified its path forward.

“That curve continues to rise, just not at the slope that originally was projected,” Newsom said. “So let us continue in that stead, continue in that spirit to meet this moment and continue to do more to practice the physical distancing, the social distancing, that are required.”

Data compiled by this news organization shows 17,498 Californians had tested positive for COVID-19 as of Tuesday — up 7% from the day before. And 447 Californians have died after contracting the novel coronavirus.

In Alameda County, health officials reported 45 new cases of COVID-19 on Tuesday and two new deaths — bringing the total number of infections there to 602 and the number of deaths to 15. Berkeley, which tracks its figures separately, reported 32 cases and no deaths.

Illustrating the danger that remains, two Alameda County nursing facilities saw coronavirus outbreaks Tuesday — Gateway Care and Rehabilitation Center in Hayward said it may have at least 40 cases, although not all are confirmed, while East Bay Post-Acute Center in Castro Valley reported 12.

San Francisco reported 622 infections and nine deaths. The death toll in San Mateo County swelled to 21 on Tuesday, an increase of eight from the previous day, while its case count rose to 589. Contra Costa County reported 442 cases and seven deaths.

Santa Clara County reported 61 new positive cases of COVID-19 on Tuesday, bringing the total to 1,285. The county has seen 43 deaths — including one new fatality reported Tuesday.

Despite the higher numbers, some encouragement also came out of Santa Clara County: Health Officer Sara Cody echoed Newsom’s suggestion that social distancing efforts are slowing the virus’ spread. In an update to county supervisors, Cody predicted the county could see between 2,500 and 12,000 positive COVID-19 cases by May 1. While that is far higher than current totals, Cody said that if Santa Clara County officials had done nothing to intervene, the case count would be “somewhere in the 50,000 range” by May.

While she acknowledged the numbers are estimates limited by testing ability and other factors, the point was clear: “We have made a difference in the overall trajectory of cases in our county,” she said.

In early March, the number of cases in the county was doubling roughly every three days, Cody said. It has slowed to doubling about every two weeks.

“The trend is exactly what we want to see,” she said.

Cody said projections show that with the new “surge” in acute care beds added in recent weeks, there should be enough across the county’s hospital system to address the pandemic.

“Without the shelter in place, we anticipated that right around tax day we would also have run out of acute bed capacity, and by the end of the month we would have likely exceeded our acute-plus-surge bed capacity,” Cody said.

At the state level, Newsom on Tuesday stood firm in his prediction that California will see its peak surge in COVID-19 cases in late May — despite a recent, widely publicized report from the University of Washington’s Institute for Health Metrics and Evaluation that predicts an April 14 peak for the Golden State.

“When we hear of the various models suggesting that April is the time when we see that peak,” said Dr. Mark Ghaly, California Health and Human Services secretary, “we know that our efforts — and congratulations to all the Californians who are going with us in that direction to flatten the curve — that it makes a difference.”

The later the peak, the more time the state has to prepare, said Dr. Arthur Reingold, division head of epidemiology and biostatistics at UC Berkeley. Buying an extra four to six weeks could allow officials to secure enough ventilators and hospital beds, but it could also mean new advancements in COVID-19 treatments and other benefits.

“If we use the time correctly, it gives us more time at the local and state health department level to hire, train and stand up additional staff who can be available to help with follow-up contact tracing, isolation, quarantine — the kinds of things that we’re going to need to take a more targeted approach and which right now are sadly lacking,” Reingold said.

But Reingold said he’ll be the first to admit he doesn’t know whether the peak will come in a week, in late May, or somewhere in the middle. All models have uncertainty because they make assumptions that may differ from the realities on the ground. And state-wide data sets can miss flare-ups in smaller California counties, he said.

What’s more, even after the curve is flattened, California won’t be in the clear, Reingold said.

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Watch: Santa Clara County Public Health Department gives updates on reopening schools, Sept. 18 “I think the problem is, with this virus, even when the curve bends and goes down, it’s almost certainly the case that (a) vast portion of the population is still susceptible to this virus,” he said. “The virus likely is not going to disappear from the face of the earth this summer.”

To help Californians cope with the uncertainty, as well as with the day-to-day stressors of isolation and the shutdown of the economy, Newsom and Surgeon General Nadine Burke Harris on Tuesday launched an online “playbook” with strategies for reducing stress through proper nutrition, adequate sleep, mindfulness and other healthy habits.

“I just want folks to know that staying at home doesn’t mean you’re alone,” Newsom said. “As a state, we’re here to do what we can to support you and be there at a time of need.”