Vaccines are a fundamental building block of modern public health, and everyone who can should get them. But some people can't be vaccinated — very young babies, the elderly, or people who have allergies, depending on the particular vaccine. However, a rigorous vaccination program can still protect those people.
How? As Aaron Carroll explains below, it's all about the statistics of disease. In order for an outbreak to spread, there must be a transmission mechanism — typically, another person who catches the disease and then gives it to someone else. But if there are enough people who are immune to the disease surrounding the sick person, then the outbreak can't get going.
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