(CNN) Not long ago, a 4-year-old boy died of the flu. His mother, under doctor's orders, watched his two little brothers like a hawk, terrified they might get sick and die, too.

Grieving and frightened, just days after her son's death she checked her Facebook page hoping to read messages of comfort from family and friends.

Instead, she found dozens of hateful comments: You're a terrible mother. You killed your child. You deserved what happened to your son. This is all fake - your child doesn't exist.

Bewildered and rattled, she closed her Facebook app.

A few days later she received a text message from someone named Ron. Expect more like this, Ron warned. Expect more.

The attacks were from those who oppose vaccination, and this mother, who lives in the Midwest, doesn't want her name used for fear the attention would only encourage more messages.

Nothing too cruel

Interviews with mothers who've lost children and with those who spy on anti-vaccination groups, reveal a tactic employed by anti-vaxers: When a child dies, members of the group sometimes encourage each other to go on that parent's Facebook page. The anti-vaxers then post messages telling the parents they're lying and their child never existed, or that the parent murdered them, or that vaccines killed the child, or some combination of all of those.

Nothing is considered too cruel. Just days after their children died, mothers say anti-vaxers on social media called them whores, the c-word and baby killers.

The mother in the Midwest, who wants to remain anonymous, isn't alone.

Jill Promoli, who lives outside Toronto, lost her son to flu. She believes the anti-vaxers are trying to silence the very people who can make the strongest argument for vaccinations: those whose children died of vaccine-preventable illnesses.

Jude McGee, who died of the flu at age two. His mother, Jill Promoli, has suffered abuse from anti-vaxers.

Flu took the life of Promoli's 2-year-old son, Jude McGee, three years ago. She's since started a campaign in his name for flu prevention, including vaccination.

"I know that these people are really trying to hurt me, and I understand that the reason they're doing it is because they want me to stop," she said.

Anti-vaxers respond

Larry Cook, the founder of Stop Mandatory Vaccination, doesn't deny that such attacks on mothers of dead children exist.

In an email to CNN, he wrote that members of his group make more than half a million comments on the group's Facebook page each month.

"Any discussions about parents who lose their children after those children are vaccinated would be minor in number, and even smaller would be the number of members reaching out to parents in private message to share their concerns that vaccines may have played a role in a death," Cook wrote.

"I do not condone violent behavior or tone and encourage decorum during discussion," Cook wrote, adding that anyone "who deliberately engage[s] in the politics of advocating for compulsory vaccination where children may be further damaged through government vaccine mandates can expect push back and resistance, alongside knowledgable discussions about vaccine risk in social media commentary."

Cook said some of the more than 160,000 members of his group have been targets of "harassment campaigns," and that "police have actually showed up at my members' doorsteps."

He added that he's been threatened and included a screenshot of a private Facebook message that said, "Finally found where you live. Finally I'll be able to put a bullet in you. You are dead."

Another anti-vaccination leader blamed the postings on grieving parents' pages on "infiltrators" who try to "create incendiary situations."

"I tell everybody that you should look at the person you're talking to and those on the other side of this discussion and recognize that they care about children, too," said Del Bigtree, chief executive officer of the Informed Consent Action Network.

During the public comment period at a meeting last month of the US Center for Disease Control's Advisory Committee on Immunization Practices, more than a dozen people spoke about their concerns about vaccines. Some said they or their loved ones had been injured by vaccines.

"My older son suffered documented illness and regression following vaccination," said Jackie Martin-Sebell. "These vaccines are not safe for everyone."

Another speaker, Rilei Cherry, said her son developed autism as a result of vaccines. "We owe it to our children to truly look at the long term effects of vaccines and be honest about what could happen to our children," she told the CDC committee.

Despite the speakers' concerns, more than a dozen studies have shown that vaccines do not cause autism. The American Academy of Pediatrics says "Vaccines are safe. Vaccines are effective. Vaccines save lives."

Jill Promoli with her twin boys, Jude and Thomas McGee. Jude died at age two of the flu.

The mothers

On May 6, 2016, Promoli put her toddlers Jude and his twin brother Thomas, down for an afternoon nap in their home. Jude had a low-grade fever, but he was laughing and singing when he went down for his nap.

When his mother went to check on him two hours later, he was dead. Promoli said the next few weeks were "a living hell."

"Having to go in and plan a funeral and find the ability somehow to even take steps to walk into a funeral home, to make plans and decide whether to bury or cremate your child -- it was just all so horrifying," she said.

When an autopsy came back showing Jude had died of the flu, Promoli started her flu prevention campaign.

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That's when the online attacks began.

Some anti-vaxers told her she'd murdered Jude and made up a story about the flu to cover up her crime. Others said vaccines had killed her son. Some called her the c-word.

The worst ones -- the ones that would sometimes make her cry -- were the posts that said she was advocating for flu shots so that other children would die from the shots and their parents would be miserable like she was.

"The first time it made me feel really sick because I couldn't fathom how anybody could even come up with such a terrible claim," Promoli said. "It caught me off guard in its cruelty. What kind of a person does this?"

Twisted logic that relies on scientific lies doesn't bother Promoli so much anymore. She's continued with her flu shot campaign, persuading Canadian Prime Minister Justin Trudeau to publicize his flu shot.

Got this last night. Get your flu shot - for your protection and to help protect the more vulnerable people around you. #ForJudeForEveryone pic.twitter.com/2EFZJWUdkv — Justin Trudeau (@JustinTrudeau) November 22, 2018

"I've had to grow some very thick skin," she said.

She said no matter how many nasty messages she's received -- and she says she's received hundreds -- she'll continue her campaign.

"The work that we're doing might mean that somebody else doesn't have to go plan a funeral for their toddler, and that is everything," she said.

Other mothers have also persevered despite attacks from anti-vaxers.

Serese Marotta lost her 5-year-old son, Joseph, to the flu in 2009, and is now chief operating officer of Families Fighting Flu, a group that encourages flu awareness and prevention, including vaccination.

In 2017, she posted a video on the eighth anniversary of her son's death to reinforce the importance of getting the flu vaccine.

"SLUT," one person commented. "PHARMA WHORE."

"May you rot in hell for all the damages you do!" a Facebook user wrote on another one of her posts.

She says a Facebook user in Australia sent her a death threat.

"She called me a lot of names I won't repeat and used the go-to conspiracy theories about government and big pharma, and I responded, 'I lost a child,' and questioned where she was coming from, and she continued to attack me," said Marotta, who lives in Syracuse, New York.

Catherine and Greg Hughes, an Australian couple who lost their 1-month old son, Riley, to whooping cough, have also received online abuse. Too young to be vaccinated, Riley relied on herd immunity -- the vaccinations of others -- to protect him.

As his mother held his hand, Riley Hughes was baptized hours before he passed away.

But herd immunity didn't protect him, since the area where the Hughes family lived in Perth has some of the lowest vaccination rates in Australia.

"Riley's death was a very inconvenient truth for anti-vaccine activists," Catherine said. "The nasty messages started 24 hours after he died. They called us baby killers and said we would have the blood of other babies on our hands. We've been told to kill ourselves."

The couple started a vaccination campaign , Light for Riley.

Catherine said they still receive vile comments years after Riley's death.

"[F**k] you, Hughes family," one Facebook user wrote on the Light for Riley page.

"What a [f**king] evil whore you really are," another user wrote to them in a private Facebook message.

Another Facebook user was more succinct.

"Please die," the user wrote in a private message.

"A lot of them come from the position that they have children that were vaccine-injured," Catherine said. "But a fair chunk of them are just haters."

The professor

Grieving mothers aren't the only targets of anti-vaxer abuse.

Dorit Reiss, a professor at UC Hastings School of Law, has received countless vile messages, and as with the mothers, many of the messages are gender-oriented. Over the years, she's become pretty blasé about it.

"'Whore' is pretty normal," said Reiss, a pro-vaccine advocate who has written extensively about vaccines. "I've also been called a [c**t]."

Sometimes Reiss, who is Jewish, receives comments that mention the Holocaust.

One Facebook user made a meme with a photo of her father with "Proud Supporter of the Vaccine Holocaust." Reiss says her father has nothing to do with vaccines.

Another meme shows a photo of Reiss holding her infant son and it says that Reiss is "FORCE-injecting" her baby with vaccines.

Below the photo is written: "Because one holocaust wasn't enough."

Other Facebook users have said her children look sick in photos, and that vaccines are clearly to blame.

"The Boy [sic] appears lethargic," one user wrote, with "dark circles under his eyes. These are common precipitants of vaccine induced immune damage and suppression, as well as vaccine induced transient ischemic adverse event."

Of all the various messages from anti-vaxers, Reiss said the one that angered her the most was a voicemail left for her husband on his work phone.

"If I hear or see anything written by your wife after today, I will release your phone number, your work phone number, your work address, her work address, her work phone number," the caller said, correctly reciting their phone numbers and home address.

The doctors

Three pediatricians who are vocal vaccine advocates have also been frequent targets of anti-vaxers. All three now have security escorts when they speak publicly.

Dr. Paul Offit keeps a fat folder of nasty messages he's received so that "if someone kills me, my wife can give it to the police." He does not laugh when he says this.

"Rot in hell you baby killer," one user wrote in an email to Offit, who is director of the Vaccine Education Center at the Children's Hospital of Philadelphia and professor of pediatrics at the Perelman School of Medicine at the University of Pennsylvania.

"Go [f**king] kill yourself," another wrote.

Dr. Peter Hotez at the Baylor College of Medicine in Houston is a vaccine researcher who wrote a book about his daughter called " Vaccines did not Cause Rachel's Autism ."

"You have no morals whatsoever and you know that you are a [f**king] liar. I hope you rot in hell," one anti-vaxer emailed Hotez, a professor of pediatrics and dean of the National School of Tropical Medicine at Baylor.

Users on the social media platform MeWe discussed an upcoming public meeting Hotez was expected to attend.

"Maybe if we cause him enough stress he'll have a heart attack before [Wednesday]," one woman wrote, adding, "#sorrynotsorry."

Dr. Richard Pan, a pediatrician and a California state senator, spearheaded a successful attempt to get rid of vaccine exemptions for personal or religious reasons for schoolchildren in his state. He's frequently been the target of race-driven abuse by anti-vaxers on Facebook.

He says he's received thousands of hateful messages from anti-vaxers.

"Chinese garbage," one user wrote on Pan's Facebook page, followed by vomiting and devil emojis. "Most ignorant [a**hole]."

"I hope they stone you to death," another Facebook user wrote. "I'll make a special trip to happily watch your head crack. The parents of the children you are destroying should each get a chance. Like a nazi piñata."

Some of the professionals and the mothers interviewed for this story said they reported the abusive messages they received to Facebook. Most of those who made reports said they received an automated response and in the end nothing changed. Others said after they made a report the sender was suspended from Facebook for a short period of time, or their offensive messages were removed.

Others said they didn't report to Facebook because the process was onerous or they'd heard that it wouldn't change anything.

A Facebook spokesperson responded to these concerns:

"We try to empower our users with controls, such as blocking other users and moderating comments, so they can limit their exposure to unwanted, offensive or hurtful content. We also encourage people to report bullying behavior on our platform, so we can review the content and take proper action," the spokesperson wrote in an email.

"We want members of our community to feel safe and respected on Facebook and will remove material that appears to purposefully target private individuals with the intention of degrading or shaming them."

Erin Costello creates fake Facebook accounts so she can join anti-vaxer groups to see if members are planning to attack mothers of dead children.

The spy

Erin Costello, a former bartender and current stay-at-home mom in Utica, New York, is the "Ron" who texted the grieving mother in the Midwest, warning her to expect more anti-vaxer attacks. Costello is an administrator for the pro-vaccine Facebook page " What's the Harm?

Costello is one of several vaccine advocates who've set up so-called "sock puppet" or fake Facebook accounts and then joins the closed anti-vaxer groups to spy on them.

She said she often sees members discussing posts by parents of sick or dead children, sometimes suggesting that members "educate" those parents by posting on their page.

For example, a member of the anti-vaccine group Stop Mandatory Vaccination said a mother had posted that her baby had suffered seizures after receiving vaccines.

The anti-vaxer urged others in the group to "comment for her to read! I want to win this mom over and she really trusts her pediatrician but at the same time she is scared!"

Another member of Stop Mandatory Vaccination re-posted a post by Catherine Hughes, the mother who'd lost her child to a vaccine-preventable disease, calling for others to vaccinate their children.

"Anyone want to chime in on this post?" the anti-vaxer wrote.

Another member responded, "I feel sorry for the lost baby and her other children but someone needs to inject her with vaccines until she dies."

A mother's greatest fear

When she sees anti-vaxers talking about parents in their closed groups, Costello, the online pro-vaccine spy, gets in touch with those parents to warn them they may be getting nasty messages from the anti-vaxers.

When Costello reached out to the mother in the Midwest, she explained why she was contacting her.

"I know you're likely getting many horrible messages on Facebook right now," Costello wrote to the mother. "Children such as [yours] are the reason why I do my part to fight for overwhelming acceptance of vaccines as well as fight against the lies and misinformation that are recklessly spread around against vaccines."

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The mother wrote back.

"I appreciate the strong role you take in helping protect families like mine," she said.

After hundreds of Facebook comments from anti-vaxers, the mother turned off comments on her page, and deleted many of the ones she received.

Some are still in her head, though. She weeps as she remembers the one that was hardest to read.

"The ones that said this was a fake story. That he wasn't real. That my child didn't exist," she said. "Because when your child dies, that's the biggest fear -- that he will be forgotten."