If enough people are vaccinated, an isolated case of infectious disease will not morph into a full-blown outbreak.

This is called "herd immunity" - the unvaccinated are more protected because they aren't exposed to the disease. To achieve it, vaccination rates need to be 80 percent to 95 percent, depending on the illness.

Herd immunity relies on the effectiveness of the vaccine and how easily transmissible the disease is, said William McKinney, associate dean for research at the School of Public Health at the University of Louisville.

On the low end, herd immunity for polio is about 80 percent, McKinney said, while measles is at the high end at about 95 percent. The Star used those standards as safe levels for polio and measles vaccines.

Measles is highly infectious because it is spread through airborne droplets that remain active on surfaces for up to two hours. Polio is less infectious because it is spread through the "fecal-oral" route, where one person's contaminated feces are ingested by another person due to poor hand washing or unsanitary conditions.

Other vaccine-preventable diseases fall between the herd immunity of polio and measles, McKinney said.

For DTaP, which protects against pertussis, tetanus and diphtheria, the Star - after consulting with public-health experts - used 90 percent as a safe level. Pertussis and diphtheria are infectious because they are spread through the air by coughing and sneezing. In addition, the pertussis vaccination is effective in only about 80 percent of those who receive it, said Maricopa County Public Health Director Dr. Bob England. That calls for high herd immunity.

England said the unvaccinated serve as potential vectors for the disease, which can keep an outbreak going - a reason unvaccinated children are often removed from schools if there is an outbreak, such as a February wave of mumps in a Gilbert school, he said.

McKinney said a good metaphor for herd immunity is a herd of cattle that puts its weaker members on the inside of the group, protected by the stronger individuals on the outside. This shields the vulnerable against attack by predators such as wolves.

For people, the weaker members at the center of the herd are babies, those with weakened immune systems or whose vaccines didn't work. "Those folks are insulated from those diseases by the healthy people," McKinney said.

What exactly constitutes a herd? Basically, a group of people who regularly share the same space and circulate together, McKinney said.

For younger children - like the kindergarten classes the Star analyzed - "their classroom is pretty much the herd," McKinney said. For high schoolers, who switch classes regularly, the herd is at least as large as the grade level, and could be the entire school.

The state requires schools to report vaccine data in kindergarten, sixth grade and 10th grade. The Star chose to examine kindergarten data because those small classes most resemble a herd for disease purposes.