Meanwhile, the Democratic National Committee said there will be no live audience at the next presidential debate Sunday in Phoenix. CNN, which will broadcast the debate, said there will be no a spin room or media filing center, either.
Sanders and Biden called off rallies planned for Tuesday night in Cleveland, where they were expected to address the results of Tuesday's primaries in six other states, ahead of the Ohio primary next week.
Biden also pulled down a get-out-the-vote event planned for Thursday in Tampa, Florida, and replaced it with a speech on the coronavirus epidemic in his hometown, Wilmington, Delaware.
"Out of concern for public health and safety, we are canceling tonight's rally in Cleveland," Sanders' campaign communications director Mike Casca said in a statement. "We are heeding the public warnings from Ohio state officials, who have communicated concern about holding large, indoor events during the coronavirus outbreak."
Casca added that Sanders "would like to express his regret to the thousands of Ohioans who had planned to attend the event tonight" and that "all future Bernie 2020 events will be evaluated on a case by case basis."
The DNC said both campaigns requested that there be no live audience at Sunday's debate. "The DNC has been in regular communication with local health officials and the Mayor's office, which advised that we could proceed as planned," DNC Communications Director Xochitl Hinojosa said in a statement. "Nevertheless, our number one priority has and will continue to be the safety of our staff, campaigns, Arizonans and all those involved in the debate."
All three confirmed cases of coronavirus in Ohio so far have been found in Cuyahoga County, which includes Cleveland, prompting Ohio's governor to declare a state of emergency and advise that coming indoor events be canceled.
Biden's campaign heeded the warning, as well, with deputy campaign manager Kate Bedingfield saying the former vice president will address the media in a different format, instead.
"We will continue to consult with public health officials and public health guidance and make announcements about future events in the coming days. Vice President Biden thanks all of his supporters who wanted to be with us," Bedingfield said.
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Fears about the coronavirus have hit the election as campaigns and election officials try to balance the competing goals of connecting with voters and protecting them by keeping them isolated from potentially infected people.
Ohio on Tuesday ordered the relocation of at least 128 polling locations out of senior residential facilities, which have proven particularly vulnerable to infection.
David Pepper, chairman of the Ohio Democratic Party, said he expects canceled political events to become the new normal until the epidemic is contained.
"As people come to grips with this, I think you'll see a lot more," Pepper said of the cancellations. "This is bigger than any individual, short-term interest."
The AFL-CIO, the country's largest federation of labor unions, canceled a presidential forum in Orlando, Florida, where Sanders and Biden had both been scheduled to appear last weekend.
But Pepper said he hopes fear about the virus will not depress turnout, saying he and other officials have been advising everyone to vote early or by mail when available. "If you worried about going out Tuesday, that's why you can vote early," he said.
Washington state, which is holding its primary Tuesday, is one of a growing number of states that conduct elections entirely by mail.
A top Biden campaign official, Ron Klain, was off the campaign trail Tuesday so he could testify before Congress about his former role coordinating the Obama administration's response to the 2014 Ebola outbreak.
The Centers for Disease Control and Prevention is advising older Americans to "avoid crowds," because they're especially vulnerable, and all three major presidential candidates — Biden, Sanders and President Donald Trump — are in their 70s.
Trump has so far downplayed the risk of the disease caused by the coronavirus, and his re-election campaign said it is "proceeding as normal." But his campaign has none of his signature rallies on its schedule. A bus tour through several battleground states and a fundraiser with first lady Melania Trump were canceled, but the campaign cited "scheduling conflicts," not the COVID-19 outbreak.
Hand sanitizers, handshake alternatives and shorter rope lines have quickly become the new reality of campaigning in the time of the coronavirus.
Candidates are used to dealing with the risk of infection, because shaking hundreds of hands a day and meeting with large groups is part of the job description. Both Biden's and Sanders' campaigns seemed eager to press on as long as they could, but they said they would heed official advice.
Biden shook hands with union workers at an event Tuesday morning but was also seen doing some fist bumps and applying hand sanitizer before eating.
Democratic National Committee Chairman Tom Perez has switched from handshakes to elbow bumps, and former Secretary of State John Kerry, stumping in Florida for Biden on Monday, told a crowd that he would shake their hands but couldn't, so he instead put his elbows out and twisted his hips to do what he called the "new dance" of the elbow bumps.
Campaigns say they have not run into staffing or volunteer shortages over coronavirus concerns but are starting to think of creative ways to reach voters.
"Rallies are a great place to recruit volunteers, so that will have an impact if this continues," said Norm Sterzenbach, a veteran Iowa operative who worked for both Beto O'Rourke's and Amy Klobuchar's presidential campaigns. "Hopefully, we don't get to a point where people won't volunteer or people won't open doors. If so, I think we have much, much bigger problems."
Technology has made remote campaigning more possible, with text messaging and phone banks out of volunteers' homes increasingly common.
Beyond the presidential race, national party officials have advised down-ballot candidates to begin thinking of other ways to reach voters than in-person events.
Rep. Josh Harder, D-Calif., canceled a town hall meeting with constituents and announced that he would hold a tele-town hall instead. And Democratic Rep. Andy Kim of New Jersey canceled a rally Saturday to kick off his re-election campaign hours after state officials declared a state of emergency and confirmed the state's first death from the coronavirus.