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.