One counter-argument against mandatory vaccination from anti-vaccination groups is that if you are so concerned about measles then you can get your kid vaccinated but let me do what I want with my kid. Unfortunately, that argument does not fly for the simple reason that some people cannot get vaccinated against measles for various medical reasons, and the "herd immunity" that arises from widespread (i.e. mandatory) vaccination can protect them.
Who are these people who cannot be vaccinated against measles?
First there are those who are too young. Typically you don't receive your first shot until you are 12-15 months old, and then receive a second booster shot when you are 4-6 years old. Note that not everyone is protected after the first shot; nearly everyone is protected after the second shot. Indeed, one of the scarier stories so far was that 5 babies in a Chicago daycare center contracted measles (CNN); most likely they were too young to have been vaccinated. Second some may possess specific medical conditions that prevent them from acquiring immunity through vaccination (e.g. immune deficiency).
How does herd immunity protect those who have not been vaccinated?
According to Wikipedia, herd immunity "describes a form of immunity that occurs when the vaccination of a significant portion of a population provides a measure of protection for individuals who have not developed immunity. Herd immunity theory proposes that, in contagious diseases that are transmitted from individual to individual, chains of infection are likely to be disrupted when large numbers of a population are immune or less susceptible to the disease. The greater the proportion of individuals who are resistant, the smaller the probability that a susceptible individual will come into contact with an infectious individual."
The intuition of herd immunity is that if a large percentage of people have been immunized against measles then the probability that a person infected with measles comes into contact with someone who is not immunized is small, and this probability becomes smaller as the percentage of people vaccinated increases. As a result the disease does not spread, and instead will rapidly disappear when the afflicted individuals recover or are quarantined. Thus, the likelihood that a person who has not yet been vaccinated comes into contact with a person with measles becomes vanishingly small because there are so few people with measles.
Indeed typically the number of measles cases per year in the U.S. is under 100. Last year (2014), there were over 600 cases and this year, as mentioned above, there are already over 100 cases (CDC). This rise has been the direct result of people not being properly vaccinated.
Figure 1 illustrates another example of herd immunity this tim for the flu vaccine. In the top panel, you see that if no one has been immunized then it is highly likely that a person with flu will have contact with an unimmunized person who can then contract flu leading to the rapid spread. In the middle panel, some of the population is immunized and so the probability of a person with flu has contact with an unimmunized person is smaller than the top panel, but still significantly greater than 0, and so there is some spread. In the bottom panel, in which most people have been immunized, then a person with flu seldom contacts an unimmunized person and so flu does not spread at all i.e. the herd is protected even though there might be a few unvaccinated individuals who are unlikely to contract the disease as long as there are so few cases of the disease.
What percent of the people in a population needs to be immunized to achieve herd immunity? A Washington Post article provides a quantitative answer:
"First, we need to know what the reproduction number, or R, is. That’s how many new cases a single case of an infection will cause. Imagine that you are infected in a completely susceptible population, and you pass on the infection to five other people (i.e. R=5). In order to prevent an outbreak, at least four out of those five people, or 80 percent of the population in general, should be immune. Put differently, 20 percent of the population may remain individually susceptible, but the population would still remain protected. So if you can estimate the reproduction number for a given disease, you can calculate the fraction of the population that needs to be immune in order to attain herd immunity. For influenza and Ebola, the number R is about two. For polio and smallpox, it is around five to eight. But for measles it is much higher, somewhere between 10 and 20. And because of that, the goal for measles vaccination coverage is typically around 90 percent to 95 percent of a population."Thus, the more contagious the disease, the higher the value of the reproduction number R, which is the number of new cases a single afflicted individual will cause on average (if no one is vaccinated). Roughly speaking, you want the immunity level of a population to be greater than (1 - 1/R) so that each new case will pass on the infection to fewer than one person on average, and as a result, the disease will gradually disappear. For measles R = 20 (it is very contagious and a single person can typically transmit the disease to 20 unvaccinated people), you want to achieve an immunization of (1 - 1/20) = 95% of the population.
This is why mandatory immunization for measles is important.
Figure 1. A chart showing how herd immunity prevents the spread of a contagion like flu or measles (see main text for more details).

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