Guest Post: Herd Immunity

June 28, 2014 - 3:28 pm
Irradiated by LabRat

This is a guest post from my friend Indy, currently working on her master’s in public health after her first in biostatistics and genetics. Who is also rather fed up with seeing the concept of herd immunity abused, usually in service of justifying Why My Kid Doesn’t Need To Be Vaccinated. She’ll be around in comments to answer questions, too. Take it away, Indy.

As most of you have probably noticed, there’s been a lot of coverage in the last decade and a half about what’s politely termed “vaccine non-compliance.” What you might have missed, however, is that the tone of that coverage has started to change rather dramatically in the last few years. Media coverage in the 2000’s focused on isolated cases, the uncertainty about adverse events, vaccine schedule spacing, the theoretical link (and the disproving of said link) between vaccines and autism, and, in some cases, what the future might look like if vaccination rates continued to drop. The coverage in the past few years has been about that future – we are now living in an era of major communicable disease outbreaks. Measles, mumps, rubella, polio, and whooping cough are all making a comeback in a big, flashy way; Google any one and you’ll find at least several cities with major outbreaks going on at the moment. The World Health Organization (WHO) just declared an international state of polio emergency. These outbreaks have become international in scale and are impacting every other continent (save Antarctica) in addition to the US. (If you’d like to explore this further, check out the map here: interactive vaccine map. Start out in 2008 and then jump forward in time to 2011 and beyond. Or just look at the contrast between “all” and 2008.)

In addition to billions of dollars in health care costs, they’re taking lives; in the US, this number is currently just shy of 1400 for deaths between June 3, 2007 and June 14, 2014.1 This may not seem like many, but consider that it’s about half the number of deaths from the World Trade Center bombings. This is also approximately double the number of unintentional firearm deaths in children (ages 1-14) between 1999 and 2010, and there are massive public policy campaigns currently going on to reduce that number.1 Furthermore, this number is isolated to the US. I’m a US scientist and I work with US data sources, so I’m pretty dependent on the CDC; some countries in Europe have death tracking systems similar to those we have in the US, others don’t, and in Africa, we have to rely predominantly on WHO data. In short: given infrastructure constraints, there are decent ways of estimating how big outbreaks are in other world regions, but not great ways of carefully tracking the number of vaccine preventable deaths on a global scale. But we can conclusively say that got a very, very big problem on our hands.

This brings us to the multi-billion dollar question that’s really the point of this post: why are we suddenly seeing such massive outbreaks of vaccine preventable diseases when, in most places, the majority of parents are still vaccinating their kids? The answer, in a nutshell, is herd immunity. You’ve probably heard this term before, and many people have a general idea of what it means, although sometimes the colloquial definition is just flatly wrong. Herd immunity, in a very broad sense, is the protection granted to a few individuals without immunity when the majority of the population has immunity. In order to talk more specifically about it, though, we’re going to have to use some nitty-gritty disease science.

There are two concepts that are central to the workings of herd immunity. The first is an R0 value (pronounced “R-nought” in the world of biology and disease) and the second is an SIR model (pronounced as an acronym (S-I-R), although epidemiologists might have more fun if we’d called it “sir”). These provide two similar but slightly different ways of understanding herd immunity. Let’s start with the SIR model. SIR stands for susceptible-infected-recovered – in short, the three categories a person can fall into. You can either lack immunity to a disease, be infected with a disease, or be recovered from a disease (and thereby have immunity to it). If a disease has never been introduced to a population, everyone sits in the susceptible class. If we’re looking at what scientists call a “metapopulation” (a large population made up of small populations) a disease might have moved through some small populations but not others, so some people might be recovered, some people might be immune, some people might be susceptible. The general idea behind an SIR model of an outbreak is that eventually, every susceptible person will contract the disease, move into the infected category, and then either move into the recovered category or die. Once a disease has swept its way through a population, there’s simply nowhere else for it to go in human hosts and it dies out in that particular population. So why do we see diseases persisting over time? Firstly, because of that whole “metapopulation” thing – a disease might have burned its way through one population, but it’s probably still working its way through another, and secondly because of this pesky tendency humans have toward reproduction. When humans have babies, they’re effectively putting people directly back into the susceptible population. When that number climbs high enough, the disease is able to gain a stronghold in the population again, and you see another epidemic. This is why infections in populations tend to have a cyclic nature; time elapses and the susceptible category rebuilds itself. If you’re interested in a real world example, San Juan Pueblo in New Mexico can provide one.3 (Full disclosure: this example and the citation are from a human biology course I took a few years ago.) Smallpox first broke out in San Juan Pueblo in late 1700s (around 1780). Another major epidemic occurred about 35 years later – enough time for the susceptible population to have built up again. So what does all this have to do with vaccination? Vaccination performs a neat trick – it moves people in the susceptible class directly to the recovered class, completely skipping the infected stage. In this way, we can move babies and children directly from susceptible to “recovered” (or immune) and the susceptible population never moves above a certain level. The majority of our population is immune, the susceptible population is too small for diseases to move in, and we’re safe. Phew. But why does the size of the susceptible population matter? Here’s where we get to R0’s.

An R0 value is the basic reproductive number of a virus or bacterium – it’s the number of people an infected person will infect provided that no one around them has immunity. It’s a shortcut for understanding how rapidly a disease can spread through a population. There are a lot of parameters that go into this value, depending on things like population density and disease dynamics, but the long and short of it is that some diseases have higher R0 values than others. Most of the “big bad” diseases that are vaccine preventable have really high R0 values; measles can be as high as 18, mumps can reach 14, rubella’s high is 16, and pertussis’ (whooping cough) is 18. The 1918 flu (as bad as it was) had a maximum R0 somewhere around 3, so even diseases with relatively low R0 values can be major problems if the majority of the population is susceptible.2 It’s worth noting that similar data aren’t widely available for many common domestic animal diseases, but rabies has an R0 of around 2 (not surprising given that its method of transmission is the rare act of biting). Scrapie (a sheep disease which involves, well, the delightful case of sheep eating other sheep bits) has an R0 around 4.5 It’s reasonable to assume based on human diseases that spread in similar ways that respiratory viruses such as distemper and viruses that are spread via surface contact (such as canine parvovirus and feline panleukopenia) have higher R0 values than these; these types of diseases are referred to as “highly contagious” across veterinary literature. A Swedish study in the 1980s on canine parvovirus infection found that epidemics of parvo could continue as long as there was a concentration of 6 unvaccinated dogs per square kilometer.6 Given this, it’s starting to seem obvious how big outbreaks can start. One person infects 18 others? That’s a fast moving disease. So what do you do with a disease like measles? How do you stop an R0 of 18? (How do you solve a problem like rubella?) In short: you make sure every person the infected case has contact with can’t catch the disease. This is herd immunity. If a person with measles would infect 18 people, but all 18 of the people who might become infected are immune, the chain of infection stops with that individual. No one else gets measles, and there is no outbreak. This is a great thing from a public health perspective, but it’s a really crappy thing from a vaccine compliance perspective. In order to achieve herd immunity for diseases like measles, mumps, and polio, vaccine rates have to be above 90%. (Sometimes it’s more in the neighborhood of 95% – diseases with high R0 values are incredibly hard to stop in their tracks.4) (As an aside, this number is the “critical proportion”, “pc”, or the minimal immunization coverage needed in a population to eliminate infection. It’s found as the simple equation [MATH] 1-1/R0. [/MATH] Sorry for the equation.) As vaccination rates have dipped, diseases are able to gain a foothold. We have a two-fold problem on our hands: the susceptible population is too high, and we have diseases with really high reproductive numbers that can infect very large numbers of people. Diseases jump back into populations, find a big, thriving susceptible population, and start infecting away. Voila: you have yourself an outbreak.

So why is herd immunity such a hot topic, given all of this crazy disease math? It’s because most people have very mistaken ideas about susceptible population sizes, R0 values (if they know what they are at all), and needed vaccination rates. Most people think that if we vaccinate the majority of people (oh, say, 50-60 percent) then their kids (or themselves, or their dogs, or their pink flamingo lawn furniture) will be protected by the nebulous “herd immunity.” (This, by the way, is why when Amanda Peet called parents who didn’t vaccinate “social parasites,” I agreed with her. Sure, it was a rude way to phrase it, but it’s exactly what’s going on – people are relying on others in the community to keep themselves safe and to derive benefit.) But sadly for them and even more sadly for everyone else, that’s just not how it works. When we need vaccine compliance rates of 95%, everyone has to vaccinate to keep the susceptible population low enough. But, but, but, someone out there is starting to say, there’s still 5%! Can’t I be in that 5%? Firstly, everyone thinks they can be in that 5%, then we end up with really low vaccination rates and the same problem to begin with. And secondly, the medical community needs that 5% buffer because not everyone can be vaccinated. People with compromised immune systems. (See: children with leukemia.) People who are actually allergic to vaccines. People who have chronic infections. Cancer patients. Some AIDS patients. That buffer is being used, and it’s being used by people with a significant need to avoid vaccination. So in short: herd immunity is not going to provide protection, and lack of vaccination has lead to its failure over the last decade or so.

There are a lot of reasons to vaccinate your kids, self, dog, and pink lawn flamingo. Some of them are medical. (You don’t want polio.) Some of them are logical. (There is no link between autism and vaccines, and vaccine side effects are exceedingly rare – the likelihood of having an adverse event is much lower than your likelihood of getting measles if you don’t vaccinate.) Some of them are ethical. (You don’t want to give measles to a childhood cancer patient.) Some of them are social. (Most public health professionals, myself included, believe that we have an ethical obligation to the communities that we live in to vaccinate.) But this one is, simply put, mathematical. We have to keep the susceptible population low enough to prevent outbreaks, and we’re not doing it. It’s putting people in very real danger for no real benefit. So vaccinate your kids, yourself, and your pets. (And now that you understand all this epidemiology math, explain it to people on airplanes. You’ll be doing the world a favor, and they’ll leave you alone with your book.)

1a. There are a couple of sources for vaccine mortality data. I’m using anti-vaccine body count, which is calculated from CDC’s weekly morbidity and mortality reports, but CDC Wonder’s Mortality database would provide the same data. And would be named after a slightly less inflammatory celebrity.

1b. Gun death statistics are from CDC Wonder.

2. Data here are predominantly from our friend the CDC again, with the exception of the 1918 flu number which is from Fraser et al. 2009. “Transmissibility of 1918 pandemic influenza”. Nature 432 (7019): 904–6.

3. Aberle SD, et al. 1940. “The vital history of San Juan Pueblo.” Hum Biol 12: 141-87.




13 Responses to “Guest Post: Herd Immunity”

  1. Paul from Canada Says:

    Thanks very much for this! I have an colleague at work (and his wife is a NURSE!), who is anti-vac, and I have tried with little success to explain all this to him. Your explanation is simple and succinct in a way my clumsy attempts certainly are not. I will be referring people to this post.

    I grew up in Africa, and when I was a child it was still quite common to see polio victims begging in the streets, and to know that in the poor rural areas kids still died of things like measles and diphtheria.

    I remember distinctly getting my first two wheeler bike on an Easter weekend and riding it all weekend long. I woke up on Tuesday morning with severe muscle pains from over-exertion, such that I collapsed crying in pain when I got out of bed. My Grandfather found me, and the look of absolute horror on his face I will never forget. It puzzled me at the time, ’til my mom explained to me what polio was, and that when she was a little girl there had been an outbreak at her school.

    We have become too spoiled today. Anti-vac people have never known a time when childhood illnesses and simple infections killed so many. Unless we smarten up, between that and anti-biotic resistance, we may end up back in a time we thought we had left behind.

  2. Indy Says:

    It’s thought that one of the major reasons that vaccine compliance rates have dipped so low is because the current generation of young parents is the first where these diseases were held completely at bay by vaccination during their youth. My generation has never seen cases of polio or measles or whooping cough, but we have seen autism, so our risk assessment ability is completely skewed.

    I don’t think this problem is going to be around forever simply because I think the current generation of children being born is (very, very unfortunately) going to experience some of the really awful consequences of these diseases. Death isn’t the only difficult outcome – people forget that scarlet fever is what lead to Helen Keller’s blindness and deafness, or FDR’s lifelong confinement to a wheelchair. Once you’ve seen those things, I think vaccination starts to seem like more of the miracle cure that it once was and less of the lurking menace in the dark that the medical profession is trying to keep under wraps.

  3. Paul from Canada Says:


    When I was trying to discuss this with my work friend, he was talking about how “my wife sees adverse reactions all the time”, as if soreness at the injection site and mild allergic reactions, and possibly unrelated flu like symptoms were somehow worse than blindness, deafness, brain damage, sterility (mumps),and death.

    I’m not that old (45), but old enough to have a smallpox vaccination scar, and I remember having to explain to a younger girlfriend what it was. I also remember some of the photos of some of the last victims in the magazines articles that accompanied the announcement that it had been eradicated.

    Speaking of pox, how the hell did we get to the point where parents feel taking their kids to “chicken-pox parties” and deliberately infecting them with a full strength case of the disease is better and more “natural” than a vaccine? I understand that in earlier times it made because vaccines were not available and for things like mumps, it is much more dangerous for adults, and best got over with in childhood, but today?

    Being an immigrant and having traveled widely, gives me a greater appreciation for living where I do. It is hard to go all “poor me, my life is so hard, I drive a second hand car” when you have seen a real shanty town, and I think this is the same. I am aghast at anti-vac people because I have seen the alternative myself, where they have not.

    So in a way I should be GLAD that people worry about things like “vaccine side effects” rather than endemic disease, GMO “Frankenfood” and “pesticide residue” rather than malnutrition. There are even groups now against iodized salt, because none of them even knows what a goiter or cretinism IS. We don’t have rickets, cretinism, and half of every kindergarten class dead of measles etc. every year to remind us.

    The real tragedy is that a lot of these parents are sincere and really DO think they are doing what is best for their kids, but sadly, some of those kids are going to (have!) died, along with some of the 5% you so eloquently talked about who because they can’t be vaccinated, NEED the herd immunity we are throwing away.

  4. Indy Says:

    I think with chicken pox in particular there is a general feeling that it’s a very mild illness that nobody suffers much from and that the vaccine doesn’t confer great protection so you’re in real trouble if you get it as an adult. (This was true of the first generation CP vaccine, but it is now more effective to my knowledge.) People just don’t realize that even childhood chicken pox can have very serious side effects – and that there’s a decently large percentage of the adult population that’s never had it and hasn’t been vaccinated because the vaccination campaigns were aimed at kids. I knew someone whose dad got it as an adult and was in the ICU for months because he had pox lesions on his internal organs, and it’s actually worse than you’d think in terms of adverse outcomes even for children. People just don’t know.

    And yes, agreed – if I had another post, I’d discuss how the epidemiological community’s “lingo” has been pretty well co-opted by anti-vaccine folks. The CDC has VAERS, the vaccine adverse event reporting system, which, as you pointed out, people take raw numbers from and go “adverse events OMG!” and think that thousands of people are having adverse events. Well, they are, but adverse events as defined by the reporting system include dizziness and soreness at the injection shot. (I don’t, but I know a hell of a lot of people who feel faint at the sight of needles, and there’s no way of distinguishing that from an actual vaccine event short of a placebo study which aren’t really usually particularly ethical to do with vaccines.) There ARE a lot of adverse events associated with shots – but the percentage of those adverse events that is serious is tiny, and furthermore, many of those “major” adverse events may be unrelated and just a case of bad timing. I have seen every sham article out there on the dangers of Gardasil, and it drives me crazy. Any vaccine (or batch of a vaccine) that truly wasn’t safe would be pulled off the market immediately, and the CDC/FDA truly has a hair trigger when it comes to things like this; the “bad” batch of flu vaccine that had the potential to cause an increase of guillain-barré was yanked immediately, then subsequently proven to be perfectly safe. The system is set up in a way to minimize public risk. People just need to understand the system.

  5. Ritchie Says:

    I’ve been referring to this effect as it applies to firearms ownership and concealed carry, but called it the “vaccination effect”. Now I know the proper term. And voluntary non-participants are still freeloaders.

  6. Old NFO Says:

    Very well done Indy! And the sad part is that celebrities have co-opted the message without any real knowledge and continue to expound their crap to the low information generation. THAT more than anything else has led to the problems here in the states. In the middle east, AQI/Taliban/religious extremists are simply killing the vaccination providers as a way to stop it. Having been military and traveled the world, I’ve hand more damn shots than I want to think about, but having seen the results of breakdowns in herd immunity around the world, I’m not complaining. (and my newest grandson is getting all his shots on the standard timeline)…

  7. Indy Says:

    I don’t really want kids, but if I had them, I’d vaccinate on the recommended timeline. (BUT IT’S SO EASY TO SAY IF YOU’RE NOT A PARENT. Well, I’d happily volunteer up any of my nearest and dearest for vaccination on an appropriate timeline if asked, although sadly they’re all autonomous adults whom I cannot force to get vaccines. Thankfully they’re sane and receive them when needed.) I attempt to put my money where my mouth is by vaccinating my dog as requested by my vet and by vaccinating myself on a recommended schedule. I have all the appropriate “optional” vaccines – HPV, meningitis, flu shots yearly. Guess what! I am doing just fine. (And I was even one of the kids who got the “bad” batch of oral polio vaccine that caused some trouble about 20 some odd years ago.) Anecdotally, my N of 1 is just fine. And since anecdotes are now proven medical science, Jenny McCarthy can kiss my ass.

  8. Mark D Says:

    I’m 51, and I’m among the last generation of people who had the “childhood” diseases (measles, rubella, whooping cough, mumps, chickenpox). I was vaccinated for smallpox and polio, partly because it was a requirement to get into school and partly because both of my parents knew people who contracted both of those diseases when they were kids (both parents born in 1919. Yeah, I was a late-age baby). Measles etc were considered a normal part of growing up.

    I guess there were vaccinations available at the time (I was born in 1963, a quick Wiki search says that’s the year the measles vaccine first became available), but no one I knew of got them, and I and all my friends spent some time being miserable.

    No kids myself, but if I did have any they’d be vaccinated. Then again, I have a basic understanding of math and statistics.

    Re: Jenny McCarthy, I fail to see how someone whose claim to fame is willingness to disrobe and be photographed makes one a medical expert.

  9. tweell Says:

    My uncle was waving Jenny McCarthy’s book around and stating that my son’s mild autism was because of vaccinations. I argued it with him off and on for days (I take care of him, he’s a legally blind cardiac diabetic cancer survivor). He’s also autistic, they just didn’t diagnose that sort of thing in North Dakota 70+ years ago. It runs in the family (guys, anyways).

    Mild autism is handy to have IMO. The ability to shut off hearing, smell and most touch, tunnel vision and just FOCUS helps immensely with a lot of things.

    Me, I’m glad my children didn’t suffer through measles, mumps and chickenpox like I did. I was one of the few that had complications from the oral polio vaccine when it first came out (I think mine was a test batch), was partially paralyzed for months as a child, and still insisted my kids get it. Get your flu shot too, people!

    The anthrax vaccine given to military did a number on a couple friends, I’m not sure that one was ready for prime time. I still wish I’d gotten it.

  10. SJ Says:

    I am in my 30s, and had chicken pox as a child. (None of the others ones, though.)

    My Mom, who was a non-practicing RN at the time, changed her mind about vaccines for their last child. (Said youngest child is slightly more than half my age. Due to child-spacing, only the youngest child was put through the mostly-non-vaccinated pathway.) That child suffered from whooping cough somewhere before age 3. I didn’t hear any discussion inside the family about this event, so I have no idea whether my Mom un-changed her mind about vaccines.

    However, the whole family got a chance to visit Tanzania about a decade later. And everyone got vaccinated up the wazoo for everything that the CDC recommends for East Africa.

  11. Joseph from IL Says:

    No Jenny McCarthy defenders?

    Good. She doesn’t deserve defending for the damage she has already done.

    While I accept the gist of the article, I think there are a few cases not mentioned in the article.

    1) Cases where the vaccine is ineffective and does not confer immunity. These are very rare cases where the individual’s body chemistry fails to produce the antigens during vaccination. It is non-zero and also why the herd immunity portion is very important.
    2) Cases where the individual cannot take the vaccination due to serious allergic reactions to the vaccination. For instance, my grandmother (96) is allergic to eggs. Therefore, she cannot have the standard flu vaccine (the virus is incubated in chicken eggs). I have been suggesting to my mother (who is vehemently anti-GMO anything) that she recieve the flu vaccine that is not incubated in eggs. However, some anti-vax a-hole has labeled the vaccine GMO and railed against it. (which is why I think we need to bring back public pillories, but I digress)
    Other vaccines have similar issues but do not have alternatives (hence why herd immunity is a good thing) that I am aware of to date.

    Chicken pox was a bit of overkill. But with kids spending less and less time outside and socializing, it was inevitable. I still fail to see the overarching good from it to indicate that it should be a manditory vaccination.

    Considering that McCarthy’s objection to vaccines in children is linked to a widely disproven link between Thermisol (a mercury based preservative) and autism and that Thermisol was discontinued in children’s vaccines in 2002, there is no reason (barring allergies and immunocomprimised status) to not have your children vaccinated.

  12. Jennifer Says:

    Great article. Just wondering, where does one go to have their lawn flamingos vaccinated?

  13. aebhel Says:

    Indy, if it makes you feel any better, my daughter is 3 months old and is getting all her vaccinations on schedule. It’s not fun for her or me, but I’d rather cuddle a sore, grumpy, feverish baby than lose her to pertussis before she’s in kindergarten.