The first call landed about 8:30 a.m. Tuesday, warning Bergen County, N.J., officials of a bomb inside Leonia High School.

Then the phone rang in Delaware: A caller said he was armed on the roof of Millsboro's Long Neck Elementary School, ready to harm students and staff.

Nearly 100 miles north, officials at the Chichester School District in Delaware County were told a bomb was inside one of their schools, and it would detonate in 45 minutes.

One by one, the calls hit more than 50 schools in at least six states Tuesday, prompting evacuations and lockdowns for tens of thousands of students.

None proved true.

The threats weren't identical or simultaneous, but nearly all shared two traits: They came in automated voice messages. And they created chaos.

Wary of spawning copycats, state and federal authorities are reluctant to say much about their investigations, except to say each threat is being treated as an isolated incident.

But experts who track such threats say the incidents have been spiking, fueled in part by technology that helps the culprits hide. The surge leaves school officials struggling to find a balance - determined, of course, to keep students and staff safe, but exasperated by a proliferation of extremely disruptive, costly, and almost always bogus threats.

"It's extremely difficult," said Kathleen Sherman, superintendent of the Chichester School District, where officials scrambled Tuesday morning to shuttle more than 2,000 students from six schools into community centers and firehouses. "If you make the wrong call and it's not on the side of student and staff safety, it can be devastating."

The increase in threats is dramatic, experts say. Between August and December 2014 alone, schools nationwide tallied 812 threats, according to the latest data from the National School Safety and Security Services, a Cleveland-based consulting firm. That's up 158 percent from 2013, when schools fielded 315 threats during a similar period, the firm said.

A large share were bomb scares, followed closely by shooting threats. Pennsylvania bore a bulk of them: In 2014, the Keystone State had the third most threats in the nation - at least 55, the firm estimates - trailing only Ohio and California.

In the days after last week's threats, Pennsylvania State Police were communicating with other states, a spokesman said, aware of the threats' similarities. Still, police and the FBI remain tight-lipped about if or how they may be linked.

For now, FBI agents are working alongside local authorities monitoring the threats and trying to ascertain if there's a way to identify or stop them.

"I can't go into any particulars," a spokeswoman for the FBI's Baltimore Division said in an email. "We know the public attention the threat makers are getting is creating more threats."

Research indicates that the ability for one threat to inspire others is huge - one reason, experts say, that the number of incidents may be growing.

According to a study released last year by Arizona State University and Northeastern Illinois University, researchers found that as many as 20 percent to 30 percent of shootings and violent attacks at schools are set off by high-profile incidents. But imitators emerge even when threats are false.

"Contagion is real," said Alan Kazdin, a professor of psychology and child psychiatry at Yale University. "And it's not at all restricted to any particular phenomenon."

Experts also say part of the proliferation comes from technology's growing ability to facilitate and mask threats - 37 percent in 2014 were sent electronically, including automated voice calls. Long gone are the days when threats were scribbled on bathroom stalls, said Ken Trump, president of the Ohio-based firm.

"If we see a threat on Facebook . . . or some other social-media source, the difficulty starts there," Trump said. "The person who is making those threats could be outside the school, outside the state, outside the country."

Still, experts and superintendents say most threats come from current or former students - "someone who has a connection to the school," Trump said.

A rising number are also what authorities call "swatting," anonymous threats that purposely mislead authorities into dispatching an emergency response. The threats, typically computer-generated voice messages, can come from anywhere.

In Bergen County, where Tuesday's threats forced evacuations and lockdowns in 26 schools, police traced the call to a Bakersfield, Calif., phone number but have not identified a suspect.

Prosecutors and emergency management officials routinely tell school officials to take every threat seriously. Many counties in the area have begun hosting Safe Schools Summits, annual conventions to teach administrators about the safety issues facing students each year. And the Pennsylvania Emergency Management Agency has created a bomb-threat checklist for officials to use amid an investigation.

But districts are realizing that erring on the side of caution can come with a hefty price tag.

Superintendents say they never think twice about deciding to evacuate or lockdown when a threat emerges. But the costs can sneak up: Bomb-sniffing dogs. Overtime pay for bus drivers and security guards. And dozens of hours of lost instructional time.

In the Chichester district, officials paid an extra $5,000 to cover the wages of drivers and fuel for buses during Tuesday's evacuation, said Anthony Testa, business administrator for the district.

A few hours west in Cumberland County, Carlisle Area Superintendent John Friend said his district had beefed up school security in recent years - a difficult decision, he said, amid continued budget cuts.

"Now it's a balance of 'Do we need another teacher or another security officer?' " Friend said. "I don't like the message it sends . . . but it's just the cost of doing business right now."

After the publicity about the threats last week, West Chester Area School District Superintendent Jim Scanlon called his top-level administrators together to review their emergency plans. To better prepare for any future threat, Scanlon said, he's considering a drill for a districtwide evacuation.

School systems in other states have stiffened the consequences. In Wake County near Raleigh, N.C., district officials passed a policy that will force students found to be behind any threats to pay for the costs related to any response.

Trump, the Ohio consultant, said tougher policies would help. In the meantime, he called for a sweeping probe by federal prosecutors.

Such threats, he said, "really force schools and communities to be on pins and needles."

610-313-8113@mccabe_caitlin