ALBANY — The number of confirmed coronavirus cases is growing in the Capital Region with a student at the University at Albany, a resident of Guilderland, a Union College employee, and a third person in Saratoga County all diagnosed with the disease.

As the number of coronavirus cases ballooned Thursday to 328 statewide, Gov. Andrew Cuomo announced Thursday a prohibition on gatherings of more than 500 people, meaning Broadway shows and many mass gatherings are canceled. The governor said 47 people have been hospitalized.

Even as college campuses shut down and businesses ask employees to work from home, the virus is spreading. The new diagnoses prompted Albany to cancel Saturday's St. Patrick's Day parade and forced Rensselaer and Schenectady counties to forbid visits at their respective county nursing homes. Sheriffs are limiting or barring visits with prisoners at local jails.

Union College says one of its employees has tested positive. A local official said the Union worker does not live in Schenectady County nor does another person who works in the county and who also tested positive. Schenectady County Public Health Services said Thursday night that it's working with two organizations in the county who have employees that have tested positive, but did not clarify how many cases that represents.

The news of the new infections brings the region's total number of people infected to at least five. The virus can cause respiratory problems that are almost always mild but in rare cases can be deadly.

The two people in Albany County, a Guilderland woman in her 30s and a University at Albany student, were tested for the virus earlier this week and the county learned they had it Wednesday night. County officials said the patients were tested on Monday evening after experiencing respiratory symptoms. Neither needed hospitalization.

The Guilderland school district told parents Thursday afternoon that a household connected with Farnsworth Middle School had someone who tested positive — presumably the Guilderland woman in her 30s — but that no students or staff have tested positive. The household in question has been placed under quarantine, Superintendent Marie Wiles said.

School will continue as scheduled, she said, though that may change upon advice from state and local health officials. A Superintendent Conference Day has been moved up from next Friday to this coming Monday, so school will be closed that day.

Large school-related activities and events will be canceled in the meantime, Wiles said, including the upcoming school musical, Chicago, Celebrate America at Altamont Elementary School as well as dances that were scheduled to take place Friday at Farnsworth and Lynnwood Elementary School. SAT administration scheduled for Saturday at the high school has been canceled.

"This action is necessary in order to reduce the number of instances of community contact within our schools," she said. "We want to do as much as possible to protect our students and staff as we continue to take direction from the Albany County Department of Health."

Guilderland Town Supervisor Peter Barber said he was notified of the positive case Thursday morning, and that the town's medical director, department of emergency medical services and police department are working with local and state health officials to coordinate response.

The town will be canceling all discretionary town-sponsored gatherings, including court proceedings and senior programs, until Tuesday, he said.

Albany County Executive Dan McCoy urged calm, but also said "we're alarmed, because (the patients) did not travel." County officials said the health department is working to identify people who had contact with the patients.

"This is new, but I want to tell everyone don't panic," McCoy said. "We are going to get through this."

The region's first two cases involve a couple from Northumberland.

UAlbany sent out a notification about the diagnosis Thursday to all students and staff members. The student who tested positive did not live in on-campus housing. Campus leaders say they are reaching out to students, faculty and staff "who may have come in contact with this individual."

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The infected person has ties to the campus' business building.

"Also, as a precaution, we are closing the business building today for cleaning," the UAlbany statement says. "Faculty and staff who work in this building are advised to work from home today. For those employees who work in the business building and choose to report to work, please go to the University Hall lobby to be provided with an alternative work location."

UAlbany has already decided that all classes will be held remotely once next week's spring break ends.

Albany County Health Commissioner Elizabeth Whalen said the county was in contact with local hospitals and was looking to ramp up the number of tests being done.

"As we expand number of tests, the likelihood is we will find more positive cases," she said. " This is a good thing because it gives us a better idea of how this disease is present in our community and will aid us in the mitigation efforts."

Whalen said it was difficult to say how many tests had already been done in the county because individual doctors can now order tests. The county health department only becomes aware of the test when it gets the results, she said.

As the spread of the disease grows, it is expected cases will be reported in most populated areas of the country.

In the meantime, Albany Mayor Kathy Sheehan said the city's two St. Patrick's Day parades Saturday are now canceled, in addition to other large gatherings.

"We'll be reviewing those as the public health impacts evolve," she said. "There are those who are going to be disappointed in this decision, I think we have to recognize that there's still a lot that we don't know and none of us will regret erring on the side of caution."

When asked how the two positive cases will impact local schools, Sheehan said officials are in constant communication with school districts. The mayor said that officials have to be sensitive to the fact that schools, particularly in the city of Albany, are where many children eat their meals and are cared for during the day.

Albany County Sheriff Craig Apple said his office is being inundated by calls from schools and towns requesting the New York state hand sanitizer that is being manufactured. "I don't have any," Apple said, adding that when he gets a supply he will alerting local officials. "There have been outlandish requests - in terms of hundreds of thousands of gallons."

The Waterford-Halfmoon Union Free School District sent a message home to parents Thursday afternoon that one of its employees has been asked by local health officials to enter precautionary quarantine after being "in proximity" to someone who tested positive for COVID-19. The person was showing no symptoms as of 4 p.m. Thursday, when the district learned of the news, Superintendent Patrick Pomerville said.

State health officials have set up a command post at the Saratoga Spa State Park administration building to coordinate local response efforts. Swabs taken from suspected and potential cases will be collected at the site.

The first two known local cases of COVID-19 were reported Saturday in Saratoga County. A husband and wife from Northumberland, a rural town northeast of Saratoga Springs, tested positive after the wife attended a conference in Miami where she had contact with a Pennsylvania resident who tested positive. The 57-year-old husband works as a pharmacist at CVS in Queensbury.

Saratoga County Administrator Spencer Hellwig said Wednesday evening that there had been no reported spread in the community as a result of the two local cases. But early Thursday morning, the town of Clifton Park confirmed it had a positive case in an adult resident. The Northumberland couple had gone to VENT Fitness in Clifton Park.

Warren County health officials called about 400 people Monday who picked up prescriptions from the man on March 2 and March 4, and said none were experiencing symptoms. Four CVS employees and four people who received flu shots from the pharmacist were quarantined, as well as four others who had contact with the employees or flu shot recipients.

As of 5 p.m. on Tuesday, there had been five people in Albany County under mandatory quarantine and 20 people in precautionary quarantine, according to the county. County officials said on Thursday they did not have an updated number to report as they continue to try and trace the contacts of the two patients who tested positive on Monday.

While 80 percent of people who contract the novel coronavirus will develop mild symptoms that resolve on their own, health officials are particularly worried about the 20 percent who go on to develop more severe symptoms. When mild, COVID-19 resembles a cold or flu. When severe, it can cause pneumonia, reduced oxygen flow to essential organs and even death.

Hospitals and nursing homes around the Capital Region are ramping up security measures and visitation guidelines to reduce possible contact with people at risk for severe symptoms, which includes the elderly, people with underlying medical conditions, and people with compromised immune symptoms.

Area hospitals said they’ll begin screening all visitors by the end of the week. Anyone who reports fever and/or respiratory symptoms, close contact with someone who has tested positive for COVID-19, or travel in the past 14 days to geographically affected areas will be turned away.

Bethany Bump contributed.