After months of backlogs and shortages, there are signs that access to coronavirus testing in California is improving for many people with symptoms — a dramatic change from just a few weeks ago when countless sick patients were denied tests, even in emergency rooms.

Testing sites are springing up across the state. And large university labs and hospitals, while still constrained by shortages of testing supplies, are steadily expanding capacity.

UC Davis Health, which runs one of the largest hospital labs in the region, can process 600 tests a day. That’s triple its capacity on April 1, and far better than the maximum of 80 tests a day it did in late March, said Dr. Nam Tran, senior director of clinical pathology at UC Davis Health.

“We were able to balance our testing for people who needed it the most — the sickest of the sick,” he said.

It’s not that suddenly a huge amount of tests has become available, although the number has grown as many university labs and companies have developed tests.

What appears to have changed is that fewer people are getting sick and seeking testing, which has freed some providers to better meet the needs of people who want tests. State data show a nearly 9% reduction in suspected and confirmed COVID-19 hospitalizations across the state since April 1. Also, some medical providers report that fewer people are calling in to medical advice hotlines with coronavirus-like symptoms.

But state officials say even more tests are needed.

As they consider how to ease stay-at-home restrictions, public health experts and state officials say far more diagnostic testing will be vital to halting the virus and safely reopening society. In particular, it will be necessary to distribute sufficient tests and supplies to underserved places, such as nursing homes, homeless shelters and jails.

About 12,000 tests a day are conducted across California. On Saturday, Gov. Gavin Newsom said he expects testing to more than double this week to 20,000 to 25,000 tests a day.

But state officials haven’t said how they will provide enough tests to the underserved places, where people are at the highest risk of contracting and spreading the virus.

“The goal for California is to get to a place where everyone that needs to be tested can be tested,” said Dr. Charity Dean, associate director of the California Department of Public Health who co-chairs the state’s testing task force. “It won’t mean every single person across the state is tested, but it’ll mean we can target the tests to the right place at the right time.”

If it had unlimited supplies, UC Davis could perform far more tests than it does, Tran said. But the hospital has too few of the swabs and chemical reagents needed to run the tests, which are in short supply around the globe.

UCSF is also facing supply problems. A new COVID-19 testing lab that the hospital opened in March is operating at only 10% of its 2,500 daily capacity.

“One word: swabs,” said UCSF’S Dr. Joe DeRisi. “Until the availability of swabs becomes widespread, more broad testing is going to be fundamentally impossible.”

Other academic medical centers, including Stanford and UC San Diego Health, are running a fraction of the tests they could because there have been fewer symptomatic people to test in their locations.

“There is that saying, ‘If you build it, they will come,’ and I think that didn’t happen here,” said Dr. David T. Pride, director of the molecular microbiology lab at UC San Diego.

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The reported drop in people experiencing symptoms is reflected in a decline in hospitalizations across the state from COVID-19, a Chronicle analysis shows. The number of people in the hospital confirmed or suspected of having the respiratory disease dropped nearly 9% between April 1 and 17, from about 5,400 to 4,940 .

UCSF also has seen the number of symptomatic patients calling its hotline or using their self-triage tool decrease to less than half of what it was at its peak in mid-March.

Although county health department guidelines advise testing people with symptoms, there is growing evidence that the virus may be spreading in homeless shelters and nursing homes through people who have no symptoms.

One Medical, based in San Francisco, on Friday became one of the first medical providers to expand testing to people without symptoms after seeing a drop in demand from people with symptoms. And last week, the San Francisco jail began testing everyone booked into the facility, regardless of whether they showed symptoms.

“Testing is not available to everyone in the city that’s asymptomatic, (so) we’re focusing on places where either the virus would spread very quickly or where there are vulnerable populations,” said Dr. Lisa Pratt, director of jail health services. “If we had 722 people in the jail who got very sick it could potentially overwhelm our health care system.”

Of about 70 people in custody tested since March, one has been identified as having the illness, the Sheriff’s Office reported Thursday. Some results are still pending.

Yet medical experts and advocates point to a persistent shortage of testing for vulnerable people who live and work in other high-risk group settings like homeless shelters and nursing homes.

In the rare instances when widespread testing has been done in facilities where there are outbreaks, the virus has often been found in people without symptoms. For instance, The Chronicle reported last week that none of the 93 homeless people who tested positive at the city’s largest homeless shelter this month had serious symptoms.

Outbreaks in long-term care facilities across the Bay Area have also shown how easily the virus can spread undetected in places where social distancing is nearly impossible. Although new cases reported in the Bay Area dipped last week for the first time since February, cases and deaths among homeless people and residents in long-term care facilities have risen sharply.

Dr. Teresa Palmer, a retired San Francisco geriatrician, said the city won’t be able to prevent nursing home outbreaks unless there is more widespread testing, particularly of staff members. Palmer’s mother, Berenice, is 102 and lives at the San Francisco Campus for Jewish Living, a 378-bed facility that began accepting hospital patients with the coronavirus this month.

The facility has so far received five of those patients. A staff member, who did not work with those patients, has also tested positive, nursing home spokesman Marcus Young said.

Palmer said this underscores her concern that staff members might expose residents to the virus. In a recent video chat with her mother, who worked as an executive secretary and medical assistant for 30 years, Palmer said a staff member who was helping with the call took off his mask even though he was right next to her.

Young said the employee has since been re-trained. The facility employs about 600 people and, following the city health department’s recommendation, tests only patients and residents who have symptoms, he added.

San Francisco’s health department announced Wednesday that it plans a widespread public health outreach effort to help health workers quickly test newly infected people and trace their contacts. The city’s public health lab can run 216 tests a day, but struggles with shortages of supplies.

Swabs are used to collect specimens from patients’ nasal cavities, then placed in vials with preservatives before being sent to labs. Hospitals usually order swabs in bulk for pennies apiece, for influenza and strep tests. During the coronavirus pandemic, though, they have become almost impossible to obtain.

At UCSF, DeRisi recently placed an order of what he thought were swabs from China, after being unable to order from the lab’s usual suppliers. But a package of makeup applicators showed up instead.

Abbott ID Now rapid tests, which can provide results in less than 15 minutes, are being offered in 75 locations in California, including at least a dozen Bay Area urgent care clinics. But health officials in some California counties and other states have said they received very few tests to run on the machines.

The Salinas Valley Memorial Healthcare System in Monterey County received fewer than 100 test kits this month — and six had to be used simply to verify whether the Abbott machine would give accurate results. Chief Medical Officer Dr. Allen Radner did not know whether more kits will be provided, forcing the hospital to reserve its supply for the sickest patients.

“It’s like having a sports car in the garage and no gas,” said Karina Rusk, the system’s spokeswoman. “We’ve been handed a great tool that right now can’t be used as we had hoped might be possible.”

All testing will probably need to increase in the fall when health experts expect the number of people with symptoms to rise as seasonal respiratory diseases like the flu become more prevalent. By then, large labs may need to run at full capacity, said Omai Garner, director of clinical microbiology in the UCLA Health System.

“I used to call it a sprint, but the reality is we are on one of those 100-mile ultra marathons,” Garner said. “Even if I don’t need this capacity in the summer, I’m going to need it.”

San Francisco Chronicle staff writer Kevin Fagan contributed to this report.

Catherine Ho, Cynthia Dizikes and Joaquin Palomino are San Francisco Chronicle staff writers. Email: cho@sfchronicle.com cdizikes@sfchronicle.com jpalomino@sfchronicle.com