A man had just gone on a shooting rampage in Kalamazoo, Mich., allegedly killing six people while driving for Uber. Sherry Towers, an Arizona State University physicist who studies how viruses spread, worried while watching the news coverage.

Last year, Towers published a study using mathematical models to examine whether mass shootings, like viruses, are contagious. She identified a 13-day period after high-profile mass shootings when the chance of another spikes. Her findings are confirmed more frequently than she would like.

Five days after Kalamazoo, a man in Kansas shot 17 people, killing three by firing from his car. To Towers, that next shooting seemed almost inevitable.

“I absolutely dread watching this happen,” she said.

As the nation endures an ongoing stream of mass shootings, criminologists, police and even the FBI are turning to virus epidemiology and behavioral psychology to understand what sets off mass shooters and figure out whether, as with the flu, the spread can be interrupted.

[In Kalamazoo, an agonizing wait for a mass shooter’s motive]

“These things are clustering in time, and one is causing the next one to be more likely,” said Gary Slutkin, a physician and epidemiologist at the University of Illinois at Chicago who runs Cure Violence, a group that treats crime as a disease. “That’s definitional of a contagious disease. Flu is a risk factor for more flu. Mass shootings are a risk factor for mass shootings.”

The idea is not without skeptics. James Alan Fox, a Northeastern University professor who studies mass shootings, said: “Some bunching just happens. Yes, there is some mimicking going on, but the vast majority of mass killers don’t need someone else to give them the idea.”

Confirming, disputing or further exploring the idea scientifically is hampered by the federal funding ban on gun violence research. Towers and her colleagues did their study on their own time. And there’s not even a common database or definition of mass shootings.

The Congressional Research Service uses the term “public mass shootings” to describe the killing of four or more people in “relatively public places” by a perpetrator selecting victims “somewhat indiscriminately.”

But other definitions, including those used by the Mass Shooting Tracker, a widely cited crowdsourced tally, count all shootings of four or more people, including domestic incidents and street crimes. The data Towers used was largely drawn from a USA Today database of mass killings, defined as four or more people killed by any means, although the vast majority were shootings.

Towers said shootings with fewer than four people killed, while obviously troubling, usually do not generate national news coverage and show no signs of triggering other incidents. It is the most publicized events that have brought the language of viruses — incubation periods, vectors, susceptibility — into the discussion of mass shootings, which in a metaphorical sense seem to travel as a cold does, moving from day-care settings to homes to offices.

From Columbine to Charleston, here's a look at some of the notable U.S. mass shootings since 1999. (Alice Li/The Washington Post)

In the 1980s, the violence occurred in post offices. In the 1990s, schools. Now it is mutating into new forms, such as the terrorist attack in San Bernardino, Calif., that initially appeared to be a workplace shooting by a disgruntled employee.

Researchers say the contagion is potentially more complicated than any virus. There is the short-term effect of a high-profile mass shooting, which can lead quickly to another incident. Towers found that such echo shootings account for up to 30 percent of all rampages.

But there appear to be longer incubation periods, too. Killers often find inspiration in past mass shootings, praising what their predecessors accomplished, innovating on their methods and seeking to surpass them in casualties and notoriety.

For many mass shooters, the carnage at Columbine High School is an important psychological touchstone. According to an analysis by Mother Jones magazine, at least 21 have referenced the 1999 Colorado school shooting by Eric Harris and Dylan Klebold, who killed 13 and wounded 23. The dots connect one mass shooter to another in online ramblings and manifestos going back nearly two decades.

[The haunting link between two mass shootings 40 years and 500 miles apart ]

Two months after Dylann Roof allegedly killed nine worshipers last year at a historically black church in Charleston, S.C., Vester L. Flanagan killed a Virginia reporter and cameraman on live TV. Although Flanagan did not kill enough people to qualify as a mass shooter, he was clearly inspired by them.

Flanagan, an African American, killed himself as police closed in. In a manifesto sent to ABC News, he wrote: “What sent me over the top was the church shooting. And my hollow point bullets have the victims’ initials on them.”

He said he was also influenced and impressed by Seung Hui Cho, who killed 32 people at Virginia Tech in 2007.

“That’s my boy right there,” Flanagan wrote. “He got NEARLY double the amount that Eric Harris and Dylann Klebold got . . . just sayin.”

And whom was Cho inspired by?

“Martyrs,” Cho said in a video, “like Eric and Dylan.”

Why violence spreads

Behavior is contagious. Studies have shown that watching someone yawn can make us yawn. Conference speakers who come after a nervous speaker can absorb the nervousness. Bad moods spread from boss to employee.

Researchers think violence is no different. Although it’s a somewhat recent area of focus — the Institute of Medicine held a workshop on the subject in 2012 — the evidence for contagion of criminal or dangerous behavior has lurked in academic research for decades.

Studies have shown that the aircraft hijackings of the 1970s were contagious. Product tampering — also contagious. So is highway speeding, rioting and even military coups. Contagion is especially pronounced in suicides.

Numerous studies have shown that suicides cluster, particularly among young people. It is known as the Werther effect, a term coined in the 1970s by sociologist David Phillips describing what happened after Johann Wolfgang von Goethe published “The Sorrows of Young Werther” in 1774.

At the end of the book, Werther shoots himself with a pistol. Many young men followed his lead.

In many of these events, the primary vector — what transmitted the behavior — was some form of mass media. Coverage of hijackings bred more hijackings. Coverage of suicides, particularly of famous people, had the same effect. In the month after Marilyn Monroe overdosed on barbiturates, suicides increased 12 percent nationally.

Some researchers think this loop drives mass shootings. Although FBI officials declined to comment on contagion for this article, a senior investigator in the behavioral-analysis unit has said that “the copycat phenomenon is real.”

[Database: Mass shootings by the numbers]

Columbine’s timing is important. That mass shooting occurred just as Americans were beginning to use personal computers to connect to the Web. Harris, 18, and Klebold, 17, posted rants about the world on the Trench Coat Mafia website, creating a digital footprint that has had a long-lasting effect on others.

Nearly two decades later, as a result of the Internet and the explosion of social media, the transmission of violent behavior is faster, wider and permanent. Shooters no longer need to rely on television for attention and notoriety. And they can obsessively study details from previous incidents, imitating and advancing the strange cultural script that the rest of the nation is watching on repeat.

While honoring Cho, Flanagan displayed innovations that have disturbed authorities. Besides shooting people on live TV, he recorded the shooting on his phone, then uploaded it to social media. Shooting while driving for Uber, as Jason Dalton allegedly did in Kalamazoo, had a Bonnie-and-Clyde feel, making it both retro and new. Then the Kansas shooter, Cedric Ford, shot from his car, winding up at a lawn-mower factory where he worked and gunning down more people.

“On one hand, they want to be like the people who came before them,” said J. Reid Meloy, a psychiatry professor at the University of California at San Diego who studies mass killings. “And yet they also want to distinguish themselves. It’s totally paradoxical.”

But why are some people infected, while others aren’t? “In the infectious-disease world, that’s called susceptibility,” Slutkin said.

Elderly people are susceptible to the flu because their immune systems are weaker. Mass shooters could be susceptible for a number of reasons, including social isolation, depression or paranoid forms of severe mental illness.

Some researchers wonder whether mass shootings are just another form of suicide contagion. Many mass shooters kill themselves or are killed by police.

“They are always an expression of suffering that manifests itself in a psychosocial crisis that is both homicidal and suicidal,” a recent paper in the journal Comprehensive Psychology said.

Mary Ellen O’Toole, a former senior FBI profiler who has worked on mass shootings, said, “It’s only infective if they are entertaining a similar ideation.

“You get a powerful normalization of your ideas and thoughts,” she added. “It’s like a little club where it’s an okay behavior. You can achieve something very important.”

Prevention

Millions of people are depressed, socially isolated or at their wit’s end. But only a minuscule portion of them commit rampages, which, depending on what definition is used, number anywhere from a handful to two dozen a year.

“It’s a big country,” Slutkin said. “Who knows who will pick it up or who won’t?”

Slutkin’s program, Cure Violence, employs “violence interrupters” in the United States and abroad who try to disrupt shootings and other acts of violence before they happen, stopping retaliations by mediating and diverting high-risk people to counseling, drug treatment or job opportunities. Local law enforcement agencies and the FBI are trying to do something similar for mass shootings.

The FBI opened the Behavioral Threat Assessment Center in 2010, using a multidisciplinary approach, including psychiatrists, to help identify and disrupt targeted violence. The center works with local law enforcement agencies following tips about suspicious behavior from families, friends and schools.

The center, working in coordination with other government agencies, has helped address hundreds of cases. FBI Deputy Assistant Director Timothy Slater said research is ongoing “to identify behaviors that might indicate that a person is heading toward committing targeted violence. We hope this will help educate people to see the warning signs.”

Others are looking to the news media for help, part of a new twist on an old idea.

At the request of public health officials, newspapers and other outlets have largely stopped reporting on suicides unless they are deemed newsworthy. That has helped drive down suicide clustering.

Now some are pushing a campaign called Don’t Name Them, which was started at Texas State University’s ALERRT Center, where thousands of law enforcement officers train every year to respond to mass shootings. The special agent in charge of the FBI’s San Antonio field office has publicly supported the effort.

Texas State cites Towers’s research in its plea, but she thinks the idea is untenable.

“First Amendment rights should not be infringed,” she said. “It’s not just the media. There are other factors in this.”

Like guns. Her study found no correlation between state rates of mental illness and mass shootings. But it did find that “state prevalence of firearm ownership is significantly associated with the state incidence of mass killings with firearms, school shootings, and mass shootings.”

Towers would like to continue researching mass-shooting contagion, but she is limited because of the federal ban on research funding. One question that probably needs more attention: Why do the shootings fall off after two weeks? She has a theory: News coverage and social-media postings fade.

“People get bored and move on to something else,” she said.

Until it happens again.