# The case against "herd immunity" through infection

December 21, 2020

As COVID-19 cases continue to spike and governments implement stronger and stronger restrictions, I thought it might be worth visiting an argument that I have encountered on and off over the past year. In its most basic form, the argument goes “why not simply let the pandemic run its course while protecting the vulnerable as best we can, but not worrying overly much (indeed, perhaps even encouraging) those young and healthy individuals to contract the virus in a push toward herd immunity?” At first glance, depending on which political sphere you receive your news from, that sentence might fill you with either righteousness or abject terror, but I have been struck by the lack of nuance in the way this argument is covered and wanted to dive a little deeper here. First, however, we have to take care of some jargon…

### What is “herd immunity”

The term herd immunity initially gained popularity in the context of vaccination. It was observed that one did not have to vaccinate every individual in the population to curb disease spread, but rather, the rate of the spread of disease appeared to be non-linearly related to the percentage of the population that was still susceptible. Put more simply, the number of people saved from a disease is not proportional to the number of people vaccinated: at low vaccination levels, fewer people are saved than are vaccinated because no vaccine is 100% effected; at high vaccination rates, even more people are saved because the pathogen has trouble finding new viable hosts. The key takeaway here is that eradication of a disease is possible even without vaccinating everybody.

Importantly, the percentage that is actually needed to set a disease on the path to extinction depends on two factors:

1. the social network structure in the population, and
2. how easily the disease in question is passed from person to person

Traditionally, scientists have ignored the former, assuming a well-mixedThis is just a fancy way of saying that each infectious individual has the same chance to infect any susceptible individual in the population population. In such a simplified scenario, there is also a nice relationship between the reproductive number $$\mathcal{R}_0$$Recall that this is the expected number of new infections resulting from an initial infectious individual in an otherwise completely susceptible population and the percentage needed for herd immunity $$p$$:

$$p = 1 / \mathcal{R}_0 .$$

In other words, for a disease like COVID-19 with an $$\mathcal{R}_0 \approx 3$$, we would need to have at least 67% of the population immune before the pandemic would die out.

Unfortunately, our population is not well-mixed, and this can affect the proportion needed for herd immunity in complicated ways, depending both upon the structure of the network and upon which individual is chosen as the initial case. Consider some extreme examples: if the initially infected person only interacts with one other person, a well-placed vaccine could prevent any further infection. If the contact network formed a star, on the other hand, then vaccinations do nothing beyond protecting the individual actually being vaccinated.

## Why should I* care?

* when I am a young, healthy individual

Many of the critiques I hear about current shutdown policies are based on a conception that there is very little risk involved when infected with COVID-19, so long as you are young and healthy (i.e. you don’t have a pre-existing condition that makes you more vulnerable to the disease), but this confounds the risk of death with the risk of undesirable outcomes. It is true that the death rate for COVID-19 is much lower than we initially thought (more on this later), but death is not the only outcome worth avoiding. Here are some other reasons why it might be better to avoid getting sick, if you can help it.

### risk of transmission to others

One of the reasons it is so important to reduce your risk of infection is because your choices have effects far beyond yourself. Even if you manage to avoid the above risks, every additional infectious individual in the population adds additional risk of further infections, including to those less fortunate than yourself. Importantly, many of the conditions correlated with worse outcomes from COVID-19 are not obvious when looking at another person, meaning there is no way for you to ensure you do not spread the disease to someone who might be more likely to die should they be infected. Even if the first person you infect is not at risk, we are all intimately connected with one another through (surprisingly short) chains of interactions—just think of the popular-science concept of “Six Degrees of Separation.” This close connection between individual actions and population-level consequences is the key justification for vaccination requirements in schools across the United StatesMalone & Hinman 2003.

### risk of side effects and sequelae

While about 98% of all patients with COVID-19 will not die during the course of their illness, it is important to note that death is not the only adverse outcome. SARS-CoV-2 attacks multiple organ systems throughout a host individual, affecting the lungs, liver, kidneys, heart, and brain. There is increasing evidence that even “mild” cases of COVID-19 can leave patients with serious and lasting damageFor a more comprehensive piece on this, check out this one from Science and this site compiling testimonials from individuals recovering from COVID-19. For instance, a study of 538 survivors of COVID-19, revealed that nearly half of them had persistent symptoms (usually respiratory) three months after being discharged from the hospital. Some of the side effects can be quite severe, including strokes, neurological disorder(s), kidney disease, and psychiatric disorder(s) (such as anxiety and depression), just to name a few.

Finally, though children have made up a small proportion of the total number of confirmed cases of COVID-19, those that do contract the disease have a smallEstimated to be as high as 0.1-0.5% risk of developing a complex vasculitis which is being called Multi-system Inflammatory Syndrome in Children (MIS-C).

Finally, there is the possibility of side effects that will only reveal themselves years afterwardsometimes called sequelae, or “late-effects” in medical literature. This may sound like science fiction, but is actually documented for a number of common diseases. For instance, about 1 in 10,000 individuals that have measles as children will develop a neurodegenerative disorder 7-10 years after seeming to have recovered from their illness. And individuals who have had polio can sometimes see their symptoms return more than 30 years (!) after recovering from their initial infection. Because these can be so varied and occur so long after someone is first exposed to the pathogen, we really have no idea whether or not there will be syndromes associated with past COVID infection at this point.

### risk of disease mutation

This one is a bit more abstract, but bear with me. Every time a virus replicates, there is a chance that it will make a mistake in the copy and produce a new mutation. Most of these mutations will either have no effect or be detrimental to the virus in some wayfor instance, making it less able to infect new cells, but there is some chance each time this happens that the mutation will actually make the virus worse (from our perspective). There is some chance that this newly mutated virus is better able to infect new hosts, or that it is more likely to kill those that it infects. Moreover, some mutations, such as increased spread rate, are even favored by evolution, increasing the likelihood that they stick around should they arise.

Because mutation rates are fairly constant between individual virus particles, the more viruses there are in the environment (i.e. the more people there are infected with COVID-19), the more potential there is for novel mutations to arise. Thus, it is beneficial for fewer people to get infected overall, but, in particular, it is beneficial for the population size of the virushere I mean the total number of virus particles present in the world to be small when we are implementing a vaccination campaign. This is because a smaller population size means that those rare variants of the virus that are able to evade the vaccine are less likely to exist in the population to continue spreading the disease after widespread vaccination.

### risk of death

Finally, I can’t make a post like this without noting that there is some (small) risk that even the healthy and young might die from COVID-19. I do not want to exaggerate this risk—it is less than that for influenza for individuals under 65 —but it is not 0, and when we consider that there are 275 million individuals in this age range in the US, even this small risk could tally to more than 250,000 dead.

aO’Driscoll et al. 2020
bNumbers from the 2018-19 US influenza season
c i.e. given that you are infected, you are $$x$$ times more likely to die from COVID than from flu

Age (years) COVID-19a Influenzab Ratioc
0-4 0.003% 0.007% 0.43
5-17 0.001% 0.003% 0.33
18-49 0.045% 0.209% 0.22
50-64 0.327% 0.615% 0.53
65+ 3.312% 0.831% 3.99

It is also worth pointing out that death rates are not static, and while we usually think about changes being for the better (improved therapeutics, better management, etc.), it can also change for the worse depending on the number of cases circulating at a given time. As hospital beds fill up, mortality rises because we are no longer able to provide the best possible care to all patients that need itNote that this decline in care quality actually happens before a give resource is completely used up, as doctors begin to be both overworked and possibly rationing the supplies that are left.

## Final thoughts

This is not all to say that we should all lock ourselves in our homes until a vaccine is ready for mass distribution—such a course would not be without its own costs, both financially and in the psychiatric wellbeing of the individuals involved—but what I do mean to say is that the decision of whether or not to lock down is far from trivial. Neither is is a simple case of “letting people make their own choices.” This individualistic mindset does not work in matters of public health: vaccines (and face-masks) only work if enough people participatebecause of the underlying non-linearity of disease processes.

We all have to do our part to reduce the spread of COVID-19, for those most vulnerable in our population, but also for ourselves.

The case against "herd immunity" through infection - December 21, 2020 - Matthew J Michalska-Smith