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SANTA CLARA COUNTY — Public health officials on Monday evening confirmed three more deaths from COVID-19 in Santa Clara County, bringing the total number to 13.

The number of confirmed novel coronavirus cases in the county also increased by 19 to 321. But with capacity for testing limited and the deadly respiratory disease now widespread in the county, the tally is likely much higher, according to the Public Health Department.

“Because of limited testing capacity, the number of confirmed cases almost certainly represents a small fraction of the total number of persons with COVID-19 in the county,” the department said in statement.

The public health laboratory is able to run a maximum of 100 tests per day, according to the department.

As of Sunday, the laboratory had tested 1,044 samples for 657 individuals, with a focus on those with severe illness and in high-risk, critical roles such as health care workers.

High-volume testing in the United States is handled exclusively by commercial laboratories, which are still being set up, according to the department. Those laboratories are only required to report positive tests, but the department is pushing for them to report all results.

The department on Monday also released limited demographic information about the people who have died. Men made up the majority at nine and eight had pre-existing conditions. The virus has killed four between the ages of 81 and 90, two between the ages of 71 and 80, four between the ages of 61 and 70 and one between the ages of 41 and 50.

The department said it is not releasing the location of people who tested positive for the virus.

“Our current data indicate that the virus is widespread in the county and, therefore, everyone in the county has a risk of exposure to the virus regardless of where in the county they live,” the department said in a statement.

“Every hospital in the county is caring for patients who have COVID-19,” the statement continued. “Providing information on individual cases, therefore, does not provide any benefit to the public, and may instead mislead those not living in a neighborhood with many confirmed cases to falsely think that they are at lower risk.”

Elsewhere on Monday, Alameda County reported its first death from COVID-19, as well as 16 new cases. The number of cases also increased by 25 in San Mateo County, 23 in San Francisco, 10 in Contra Costa County and eight in Santa Cruz County.

Cases nationwide have topped 33,400, with more than 400 deaths, according to the CDC.

Local and state officials have taken steps in recent days to slow the spread of the virus, including orders for residents to remain home except for essential work, food and other needs.

Check back for updates