Interestingly, the first time I heard about the concept of herd immunity was in Game Theory. We discussed a scenario where for each person, getting vaccinated meant a certain risk: mathematical probability of getting sick/dying from the vaccine, and your chance of getting the disease depended on how many people got the vaccine. I thought the idea was fascinating- so you can risk whether you want to get the vaccine or not, which although it carries a certain danger, and if you get the vaccine, you are probably going to be a-ok. On the other hand, even if you were lazy/scared and didn't get the vaccine, but enough people around you had gotten the vaccine, you might be protected.
Since no vaccine is 100% effective, some individuals in a population, even if they are vaccinated, may not be protected against the pathogen. Or they may not be vaccinated, period. However, if enough people are vaccinated in the population, the pathogen can't find a host, and won't get around to infecting those who are even susceptible! This is called herd immunity. Neat, right?
It means that a population doesn't have to be 100% vaccinated in order to eradicate a disease. However, we like to leave those unvaccinated percentages for those who are immune compromised or have otherwise similar conditions that would make vaccination unwise.
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