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A Virginia mother and her three children have been removed from local and national missing persons databases, weeks after her husband said they weren't missing and that he wasn't "concerned" about their safety.

Lauren Elizabeth Tousa Cook, 30, and her three children — Benjamin Cook, 7, Hannah Cook, 5, and Elijah Cook, 2 — traveled to New York on a pre-arranged trip over Labor Day weekend, according to a statement from the Franklin County Sheriff’s Office that was obtained by PEOPLE on Tuesday.

However, instead of returning to Franklin County, the sheriff’s office said they traveled to another state, "where they have decided to remain for the time being."

"After not returning to their Franklin County home, limited contact with family, and then missing a court appearance, the circumstances met criteria to issue a missing persons alert for the family," the department said.

Authorities previously said the missing persons investigation was initiated after Lauren — who missed a scheduled court appearance at Franklin County Juvenile & Domestic Relations Court on Sept. 5, the day she was last seen — did not appear for a rescheduled court appearance on Sept. 13.

"Since that alert was issued, law enforcement has been able to corroborate sightings of the family via surveillance footage and video calls to determine that they appear to be safe and not under any type of duress," the sheriff's office said in Tuesday's statement.

The sheriff’s office said that the missing persons alert had been closed "because the elements of the investigation do not meet the criteria needed to extend a missing persons entry."

The update came two weeks after her husband told ABC affiliate WSET-TV that his "wife and children are not 'missing.'"

"I have no reason to be concerned about their safety or well-being," he told the station. "I have heard from my wife, and I'm sure she and my children are doing well. We ask that our family's privacy be respected at this time."

It remains unknown why Lauren and her kids did not return home or why Lauren was scheduled to appear in court. However, she told WSET-TV on Sept. 28 that the ordeal began after an anonymous report of alleged child abuse to the Virginia Department of Social Services.

The details of the report are not known, but according to WSET-TV, Lauren and Jordan Cook, her husband, have denied the allegations.

The Virginia Department of Social Services and Franklin County Sheriff’s Office did not immediately respond to PEOPLE's requests for comment. PEOPLE has been unable to contact Jordan Cook.

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Lauren told WSET-TV that an attorney told her that she could go on the scheduled vacation, but she decided to continue the trip after obtaining more legal advice. According to the report, her husband's lawyer said their social services case had been dismissed.

The sheriff’s office thanked the public on Tuesday "for their assistance in spreading the word about any missing person cases, and for reporting any tips that may lead to the location of that person."

The "end goal" is to "simply locate the individual to ensure that they are safe," the agency added.

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