(CN) – Dealing a blow to vaccine opponents, a California appellate court upheld a 2016 state law repealing the personal belief exemption to California’s immunization requirements for schoolchildren.

Four California parents and a California anti-vaccine group called A Voice for Choice, Inc. sued the state’s education department over the statute last year, claiming it violated their rights to due process, privacy, a public education and free exercise of religion under the California Constitution.

But in an unpublished opinion issued Tuesday, the Sacramento-based appellate court rejected each of their claims as unsupported by case law.

“Plaintiffs’ arguments are strong on hyperbole and scant on authority,” Associate Justice Ronald Robie wrote for the court’s three-judge panel, adding, “Plaintiffs’ failure to cite or even acknowledge the seminal cases (Abeel or Zucht) directly on point and counter to their argument in their opening brief violates counsel’s duty to the court.”

In an email Wednesday, plaintiffs’ attorney Brad Hakala said his clients were “tremendously disappointed” by the ruling.

“We believe that the court of appeal, in issuing their opinion, failed to fully address all of the constitutional issues, as set forth within our documents,” said Hakala, who practices in Long Beach. “The right to attend school in California is fundamental. So is the right to privacy, especially for medical records. This decision, if upheld, forces children and their parents to jump through tremendous obstacles before exercising their fundamental right to attend school, which would also include the necessity to disclose their confidential medical records.”

Governor Jerry Brown signed SB 277 into law in June 2015 after a measles outbreak that began at Disneyland infected 147 people, 131 of them in California.

Medical researchers attributed the outbreak to the high number of unvaccinated children in the region.

The law requires parents to immunize their children against 10 diseases, such as measles and whooping cough, before they can enroll in public school, unless they have a medical exemption.

Vaccine opponents have claimed vaccination is responsible for a slew of childhood issues, including autism.

The Centers for Disease Control says the evidence doesn’t support such beliefs, and that the benefits of vaccination far outweighs the harms.

“Some people have had concerns that ASD [Autism Spectrum Disorder] might be linked to the vaccines children receive, but studies have shown that there is no link between receiving vaccines and developing ASD,” the CDC says on its website.

Upholding a Placer County state court ruling against the plaintiffs Tuesday, Robie relied heavily on Brown v. Smith, in which a different California appellate court rejected similar constitutional challenges to SB 277.

The 2018 decision noted that “compulsory immunization has long been recognized as the gold standard for preventing the spread of contagious diseases,” and that “‘[s]tudies have found that ‘when belief exemptions to vaccination guidelines are permitted, vaccination rates decrease,’ and community immunity wanes if large numbers of children do not receive required vaccinations,'” Robie wrote, quoting Brown.

Based on these findings, Robie rejected the plaintiffs’ due process argument that less-restrictive means than SB 277 exist to achieve higher vaccination rates, such as public education efforts and the distribution of free medication.

And he concluded that the plaintiffs’ “liberty interests” don’t outweigh California’s interests in containing disease.

“It is well established that laws mandating vaccination of school-aged children promote a compelling governmental interest of ensuring health and safety by preventing the spread of contagious diseases,” Robie wrote, referencing both Brown and Whitlow v. California Dept. of Education.

Whitlow, another California appellate case, found in 2016 the state was “well within its powers to condition school enrollment on vaccination.”

Associate Justices Louis Mauro and William Murray also sat on the panel.

The education department had no immediate comment, and the state attorney general’s office could not be reached.

The CDC has reported 15 outbreaks of measles so far in 2018. Most occur in communities with large numbers of unvaccinated children, or are sparked by international travelers.

Last year, an outbreak of measles was reported in a Somali-American community in Minnesota with poor vaccination rates. Spurred by anti-vaccine groups who told Somali community members that vaccines were linked with autism, the outbreak soon grew to 75 reported cases.

Vaccination has reduced measles infections in the United States by 99 percent, the CDC says. Before the measles vaccination program was launched in 1963, an estimated 3 to 4 million people contracted measles each year in the United States – and up to 500 died, according to the CDC. About 48,000 were hospitalized, and 1,000 developed encephalitis, or brain swelling, from the illness.

On Tuesday, The New York Times reported at least 36 children had contracted chickenpox at a private school in Asheville, North Carolina. The school has one of the state’s highest rates of religious exemptions for vaccination, the Times reported.