Part of the difficulty in making a case for universal vaccination against dangerous disease is a lack of understanding of probability. Since there are few certainties in life, except its eventual end for individuals, we are constantly calculating probabilities. What is the probability that I will get to the other side of the street before that oncoming car arrives? What is the probability that the wheel stop on my number or that I will draw the card needed to complete my hand? What is the probability that the game I am going to attend will occur or get rained out? And, of course, what is the probability that the suggested intervention will cure my disease rather than kill me or leave me permanently debilitated?

Some probabilities are more difficult to calculate than others: what are the odds that I will die from prostate cancer, and what are the odds that the operation will leave me impotent? how do I calculate the best course when my choices are an operation with an 80 percent success rate that leaves another 15 percent paraplegic and 5 percent dead? How about the same operation with 93 percent success, 5 percent paraplegic, and 2 percent dead?

The more complex the alternatives, particularly when they are being balanced against complex outcomes from non-intervention, the more difficult it is for us to make a rational decision.

That leads to a discussion of vaccination. Let’s consider a disease such as smallpox, which has killed 100s of millions of people. Not everyone got smallpox. Not everyone who got smallpox died from it–estimates are that about 30 percent, or 3 out of every 10 died. Now, consider that not everyone who gets a vaccination gets 100 percent immunity. Some people get partial immunity. Some very small percentage may not produce antibodies in reaction to the vaccine. Some people actually die of the side effects of the vaccination.

As an individual, you might think, well, it’s not great but 70 percent odds of surviving are better than none, and maybe it will miss me altogether, so why should I vaccinate? Of course, smallpox has been eradicated, and we don’t have to make that kind of determination any more since the dangers of side effects from the vaccination exceed the danger of contracting smallpox, particularly in the United States where the last documented case appeared in 1949.

If you were a free individual, not part of a society, not part of the possible transmission stream of a disease, then no one is likely to care too much what you decide? However, if you are reading this, you are part of a society providing this message to you via a societal mechanism. As part of that society, you have obligations to others in the society, including children, yours and others, who once were considered private property but are now considered individuals with rights, albeit limited compared to adult rights.

The concept of “herd immunity” goes directly to the questions posed and to your obligations within the society.

Those who are vaccinated provide a barrier to illness for those who are not:

Consider:

Assume you have 5 friends who do not know one another, and that everyone has 5 such friends.

Assume that vaccinations give almost 100% immunity and that the corresponding disease gives almost 100% probability of infection if you come in contact with a person who has it.

Now, if 80 percent of people are immunized against the disease, it is quite possible that one of your friends is not immunized. However, if 80 percent of that person’s friends are immunized, there is now only 1/5 times 1/5 or 1/25 = 4 percent chance of the disease vector reaching you. It may be that you friend’s friend has friends with 100 percent immunity, all five of them immunized, and the further you are socially from the source of infection, the lower your odds of becoming infected–even if you are not immunized. You are protected by herd immunity.

However, consider if only 60 percent of people are immunized, then 2/5 times 2/5 is 4/25 or 16 percent chance of becoming infected. That is 4 times your chance of infection from a secondary friend, as in the first example. The degree of herd immunity is a complicated calculation depending upon the percent immunized and the way the disease is transmitted. Your chance of infection depends on those factors as well as your social distance from the source of the infection.

For an animated look at the concept, click on “Play Animation” in the three scenarios of The History of Vaccines: Herd Immunity.

Here are the thresholds for different diseases as estimated by the Centers for Disease Control (CDC):

Think about flu shots for a moment:

1. The vaccine is based upon recent mutations of the virus, so you might catch a virus that is not part of the vaccine.
2. Not everyone gets 100 percent protection from a vaccine–it may be sufficient to protect against some strains and give partial protection against others
3. In part, because of herd immunity, not everyone exposed to influenza is infected

So, we have friends and relatives drawing the wrong conclusions (e.g. the vaccine caused me to get influenza), based on an association of factors that are coincidental or subject to an alternative explanation, such as a new strain or partial immunity. For most young people, the flu is an occasional inconvenience rather than life-threatening; however, their failure to vaccinate exposes others whom they could be protecting by a simple annual injection. Let’s spread the word–it might not save those young individuals–just an older person, or an asthmatic standing close to them.