The term “herd immunity” elicits strong responses from some in the anti-vaccine camp. Perhaps some do not like the use of the word “herd” because of its association with sheep, or other such animals that do the bidding of their herders. Or perhaps, and this is my belief, it is because the very idea of herd immunity rests upon the premise that vaccines are effective at stopping disease progression, and vaccine efficacy is one of the major things anti-vaxers deny.
Many times they demand proof that herd immunity exists. In and of itself, that request is not unreasonable. After all, scientific proof is the standard by which we measure claims; so what sort of support is there for the idea of herd immunity?
What is herd immunity?
First and foremost let us quickly define what herd immunity is. Basically the idea of herd immunity says that in large groups of individuals, in regards to contagious diseases (those that spread from individual to individual), if a large enough number of individuals is immune to the disease, the chances that a chain of disease transmission will be interrupted are very high, resulting in self-contained, small outbreaks that will die out quickly. Thus, even individuals that are not immune will be protected by the wall that is set up by the vaccinated ones. The herd’s immunity shields those that have no individual immunity.
The herd immunity threshold (the number of immune individuals in a herd at which level the disease cannot persist) varies depending on how contagious the disease in question is, how efficacious the vaccine is, the exposure rates etc. For example, the herd immunity threshold for pertussis is 92-94%, whereas for diphtheria it is 85%.
Here is a nice infographic from the National Institute of Allergy and Infectious Diseases showing the concept of herd immunity at work:
Credit: NIAID
The Idea of Herd Immunity Makes Sense
Let us think of two extreme scenarios.
Scenario 1 – No One is Immune
If 100% of the population has no immunity, the disease will spread rapidly. Everyone who is exposed will get sick, and besides those individuals who are completely isolated from society, everyone will get sick.
Scenario 2 – Everyone is Immune
If 100% of the population is immune, the disease will not spread and it will die off quickly. Every person who is exposed to it will be safe and no one will get sick.
Reality
In reality, the level of immunity in a given population, a.k.a herd, will be somewhere in between 0% and 100%, and the level of disease spread will be somewhere in between “everyone will get sick” and “no one will get sick”. In other words some will get sick. The closer you are to either extreme scenario the closer the “some” will be to that extreme’s outcome. Therefore the less people are vaccinated, the more the disease will spread. Vice-versa, the more people are vaccinated the less the disease will spread.
So from a logical point of view, if you accept that vaccines are efficacious in protecting against disease, you must reach the conclusion that herd immunity must exist, to some extend.
But what kind of proof do we have that in reality such protective effects do exist whenever we vaccinate large numbers of individuals?
The Math of Herd Immunity
Now, some folks can doubt the idea of herd immunity, but I think they will not doubt math. We can infact use math to come up with a formula for herd immunity. Here are the details:
R0 (The Basic Reproduction Number of the disease) - The average number of other individuals each infected individual will infect in a population that has no immunity to the disease. (for example, each infected individual on average will infect 13 others)
S - The proportion of the population who are susceptible to the disease, i.e. neither immune nor infected (for example, 15 % of the population)
In order for a disease not to die off, at the very least each infected individual should infect another individual. Now, R0 tells us the number of people that our infected person would infect, if everyone he came in contact with had no immunity. However in real life some of his contacts will be immune, and only S of those contacts will have no immunity. So our infected individual will come in contact with S vulnerable people, of which only R0 will get infected. Since we said that we need at least 1 new infection to keep the disease spread alive that means that:
R0 x S = 1
Anything above 1 and the disease will grow and become an epidemic; anything below 1 it will eventually die off.
Remember, what we’re trying to calculate is the herd immunity threshold. Let us denote that by HI. Keep in mind that HI denotes the percentage of the population that is immune to the disease (for example 78% or 0.78). Also keep in mind that S denoted the percentage of the population that is not immune to the disease (for example 22% or 0.22). Therefore, if we add HI and S up we get the full population, which in percentage terms is 1.
HI + S = 1
Or, alternatively:
S = 1 – HI
Substituting (1-HI) for S in our first equation you get:
R0 x ( 1 – HI ) = 1
Solving for HI in this equation give us:
HI = 1 – 1/R0
So let’s assume that for disease X, R0 = 10. In other words if everyone was not immunized, an infected person could be expected to infect another 10 people. This formula would tell us that the Herd Immunity threshold would have to be:
HI = 1 – 1/10 = 0.9 or alternatively 90%
If we assume that vaccine efficacy is 95%, this would mean that we would have to vaccinate at least 95% of the population to reach the required herd immunity threshold (because 0.95 * 0.95 = 0.90).
And there you have it, an admittedly over-simplified, bare bones, dirty calculation of the herd immunity threshold, and how it depends on the reproduction number of the given disease. In real life, scientists must take many more variables into account, things such as Average Age at which the disease is contracted, Average Life Expectancy etc, but this gives you a good idea of the general way in which those herd immunity levels are calculated. The numbers are calculated based on existing statistical information; they are not pulled out of thin air.
So far we’ve shown that the concept of Herd Immunity makes sense and can be derived mathematically. But we still need to show that it works in the real world. Do we have examples, studies showing the herd immunity at work?
The Scientific Evidence
Infant Rotavirus Vaccination May Provide Indirect Protection to Older Children and Adults in the United States, The Journal of Infectious Diseases, Published by Oxford University Press on behalf of the Infectious Diseases Society of America 2011. DOI: 10.1093/infdis/jir492
This is a study which looked at rotavirus discharge and cause-unspecified gastroenteritis hospital data from a sample of 1,000 hospitals in 42 states in the U.S. Pre-vaccine era (2000-2006) discharge numbers were compared with the first full vaccination year (2008) data. Here are some of the key findings, but keep in mind that, as of that time, the only age group with any significant vaccine coverage was the < 1 years old. Coverage for older children was negligible, a.k.a the other age groups were unvaccinated, thus providing an excellent test sample for herd immunity.
- Rotavirus discharges saw significant reductions. Specifically by age group:
- 0-4 – 78% reduction
- 5-14 – 71% reduction
- 15-24 – 65% reduction
- Cause-unspecified gastroenteritis discharges also saw a statistically significant reduction. Specifically by age group:
- 0-4 – 39% reduction
- 5-14 – 29% redictopm
- 14-24 – 8% reduction
How do we interpret these results? This study suggests that vaccinating children aged 1 year or less against rotavirus, provides indirect protection to other age groups not only towards rotavirus itself but also towards all-cause gastroenteritis. It appears that vaccinating young children reduced disease spread in the other, non-vaccinated groups, therefore this study provides direct support to the idea of herd immunity.
Of course, since they had only one full year of vaccination data to work with (2008) it is possible that it could have been a fluke year, an unusually low rotavirus activity year to begin with, so we must be careful not to say that this study proved the protective effects of herd immunity. As we know, one study never proves anything, and these results will need to be replicated (with respect to the rotavirus vaccine). Readers are welcome to leave links in the comments to other studies that have looked at herd immunity.
Conclusion
So how do we know that herd immunity exists?
First and foremost, if one accepts that vaccines are effective in stopping disease, it is an inevitable logical conclusion. If many, many people are immune the disease will not spread too far. Those that are not vaccinated, and are surrounded by a wall of immune people, will most likely not be exposed to the virus as the spread will stop before reaching them.
Secondly, we can show mathematically how to calculate the herd immunity threshold, by taking into account well established concepts such as the basic reproduction number of the disease.
Lastly, a study was presented that showed increased protection on unvaccinated populations after introduction of the rotavirus vaccine.
To sum it up the idea of herd immunity is biologically plausible, makes sense logically, can be mathematically modeled based on uncontroversial factors and simple algebra, and is supported by scientific observations and studies.
In other words, to deny herd immunity is to deny biology, logic, common sense, math and science, all in one swoop.
I think much of their extreme hatred of the idea of herd immunity is that it is one of the best (possibly the) arguments for making them vaccinate their kids whether they want to or not.
Not to mention that if herd immunity exists then they are very serious public health menaces and they really don’t want to think of themselves that way (nor do they want to be seen as such).
We may need >90% vaccination rates to get herd immunity, but 70% would be a solid enough majority to force the issue and I’m pretty sure we’d be able to get that kind of support.
Also, the Hutterite flu vaccine study – household/communities where children were vaccinated had fewer illnesses among the adults than other Hutterite household/communities.
It gets to the root of the fine kettle of fish and reduces your protracted term dependency on sleeping pills and sedatives. As well the functions of curing want of sleep, Zolpidem is medically proven to dilate brain functionality and improves mobility in patients pain from Akinetic mutism.
Lol!
What a load of cod’s wallop!
Herd immunity is a complete fairytale designed to sell vaccines to at least 90% of possibles ….. And you so fall for it!
If it’s a fairytale why do we observe it working?
Maybe you could point out which part of my load is “cod’s wallop” as you so eloquently put it. Please take particular care to point out where my logic went wrong, and if you are right, I will be glad to make changes to the post.
“If we assume that vaccine efficacy is 95%, this would mean that we would have to vaccinate at least 95% of the population to reach the required herd immunity threshold (because 0.95 * 0.95 = 0.90)”
Here is a major cause for concern with your thinking. We do not have to vaccinate for immunity to exist. Healthy human immune systems acquire disease, build antibodies, and the disease passes providing a LIFETIME of immunity. That is far greater in power to raise herd immunity than a vaccine that requires a booster because it didn’t do it’s intended job in the first place.
Your thinking has an even bigger cause for concern:
Which ignores that to acquire that immunity you have to get the disease in its full force (and even then you may not get lifetime immunity) with the full risks of that disease.
Vaccines at last don’t kill one out of every thousand they’re given to as diseases like measles do.
Antivaxers like to say the following:
Natural disease gives you lifelong immunity [actually wrong in many cases], therefore it is better to get the natural disease if you want to obtain good immunity (this bizarre concept means that you need to run the considerable risks of having disease in the first place…. just what we are trying to avoid through vaccination in the first place!)
Crazy.
[...] off, any parent deciding to not vaccinate their children is deciding to rely on the herd immunity of others around them — unless they plan on intentionally exposing their children to deadly [...]
Mayim, I didn’t realize chicken pox was deadly. Measles was a routine childhood disease for the our parents with minimal side effects. To exaggerate these disease as 1) deadly and 2) common in extreme side effects is poor logic.
People have indeed died of chicken pox and measles kills about one out of every thousand infected (assuming good nutrition and health care, things are much worse in the developing world).
See http://www.quackwatch.org/03HealthPromotion/immu/immu08.html for how safe the routine childhood disease of chicken pox really is.
My brother was hospitalized for chicken pox complications, as the virus affected his throat and stomach and he became dehydrated. Chicken pox can become shingles in adults who had the virus as a child, and shingles causes excruciating pain and can cause blindness if it involves the eyes. Ask my mother and grandmother-in-law about the “joy” of shingles. Pregnant women who have never had exposure to chicken pox, either by infection or by vaccination, may suffer miscarriage if they contract the virus as an adult. No, the vaccine doesn’t last an entire lifetime but that’s why we have boosters.
People with compromised immune systems will not be able to benefit from vaccines and depend on herd immunity to protect themselves. If they get an infection, it can easily become fatal.
The only reason you speak about the supposedly mild effects of these illnesses is because you are generations removed from the reality of serious infection that we can now prevent.
So from what I know you get chicken pox and then the virus becomes inactive in some nerves in our body which later in life can be reactivated and cause shingles. The chicken pox vaccine is a live attenuated form of the virus and thus would become inactive in the nerves like chicken pox and later on have the chance of reactivation and shingles. So why get a vaccine that puts you at risk for shingles later on in life when you may not have ever had chicken pox thus never having the ability to get shingles?
The vaccine is less likely to do that than the real thing and Chickenpox is still common enough that nearly everyone who isn’t vaccinated can expect to get to get it at some point.
The vaccine was introduced in the USA only seventeen years ago. So unless you are less than sixteen years old, you may already had chicken pox. My eighteen year old daughter caught it when she was six months old, and is even more likely to get shingles because she was so young.
Also, trying to be a parasite on herd immunity does not reflect well on your personality.
Sean, you don’t realize many things. Your ignorance is not a cause for celebration.
[...] [...]
[...] off, any parent deciding to not vaccinate their children is deciding to rely on the herd immunity of others around them — unless they plan on intentionally exposing their children to deadly [...]
I would be happy to send all of you who believe in the myth of vaccination a power point I created using history, evidence-based science and the governments own documents that prove what they want you to believe is far from reality. I will show you how to prevent influenza like illness (ILI) with a safe, natural and inexpensive proven method that I use. You will learn 80-85% of all ILI are not caused by Influenza A or B or the swine flu or bird flu but by over 200 other bacteria and viruses. Antibodies are temporary (2-10 years) and a CDC document states antibodies do not =immunity or protection.. you will learn there are two efficacies Research efficacy-the production of antibodies which vaccines are based on and Clinical efficacy – the ability to prevent an infection which is associated with cellular immunity, your T and B cells, not antibodies and much, much more. All work is cited. You will be truly informed after thoroughly reading every word. Than you can make up your minds. I have not been sick in 33 years. I have raised a child without vaccination and he is healthiest child I know. Sure he got sick and missed many days at school, but he acquired the diseases at the appropriate time God and nature intended and he does have lifelong immunity without the risks of vaccination. Contact me at jondavid62@ymail.com
Days he wouldn’t have missed if he had parents who weren’t negligent.
BTW: There is no god and nature does not care about us, evolution does not have any intent (though we’ll probably change that soon).
Dear Jon,
Thank you for taking the time to comment on my blog post. Please feel free to send the information to vaccinetimes@gmail.com and I will gladly review it. I would like to point out however that “he got sick and missed many days at school, but he acquired the diseases at the appropriate time God and nature intended” defeats your argument that your child is healthy without vaccines. The same logic can be used for any bad effects you attribute to vaccines “Sure she got some side effects and suffered a little but she did so at a time and manner God intended”. I’m sure you see that adds nothing to the argument, and as such should be discarded.
Anon,
To be fair, we do not know what the diseases were, so we cannot make the assumption that they were vaccine preventable, thus we cannot assign fault. It is a little bit harsh to talk of negligent parents given the info we have. Every parent is doing what they think is best for their children, including those who unfortunately decide not to vaccinate.
Thank you both for keeping the discussion going.
I think it very unlikely that there weren’t any diseases not vaccine preventable contracted by his son.
I hope you get the information Mr. David is promising to provide. I recently saw him elsewhere, he claimed: “Contact me jondavid@ymail.com and I will send you a list of 28 studies from around the world that supports Wakefields findings.” Please ask for that and compare it to these observations on studies that are supposed to independently replicate Wakefield:
http://justthevax.blogspot.com/2011/05/still-no-independent-confirmation-of.html
Though, in the same place he made this claim: “Very outdated as there are many independent studies that support wakefield’s findings and he is now suing Mr. Deer and others and the truth will come out.”
First the very outdated study was “The combined measles, mumps, and rubella vaccines and the total number of vaccines are not associated with development of autism spectrum disorder: the first case-control study in Asia”, Vaccine. 2012 Jun 13;30(28):4292-8. Apparently a study that is less than a year is outdated. Plus the lawsuit was dismissed and Wakefield keeps putting off the appeal disposition.
I will not email him, as I prefer to discuss this on an open forum where others are invited to comment. So thank you, Mr. Shaka, for taking him up on his offer.