# Is Herd Immunity A Viable Solution to COVID-19?

*This commentary was previously a part of my daily COVID19 analysis on 5/6/2020, but is presented here independently for ease of reference and to avoid re-sharing each day. As always, my training is not in epidemiology, and I defer to recognized experts for more in-depth explanations. This analysis is an attempt to convey the basic mechanics of Herd Immunity and provide commentary about whether we can anticipate it as a solution to the current virus outbreak at a level that is approachable to an untrained reader.*

Here’s my understanding of all of this, based on what I’m seeing from various public health experts and background readings. It’s an area that can be complicated with well known diseases, and with the current Coronavirus we’re still figuring some of it out.

Herd immunity (and for that matter, a lot of infection control) is based around a metric called the basic reproduction number (abbreviated “*R*0”), which reflects the number of people who are likely to be infected by a single symptomatic carrier in a populations where everyone is susceptible (the default state in most infections). For example, an *R*0 of 3 means that each infected person in a population, on average, infects 3 other people. The higher *R*0 is, the more rapidly an illness spreads. Ideally, we want *R*0to be less than 1, as this indicates that spread is slowing. Calculating *R*0 is complicated, because it reflects a product of the duration window that a person is contagious, the likelihood of infection when a susceptible person encounters the contagion (through people or otherwise), and the frequency of these contacts. This means that the *R*0 will vary between populations, and even on a day to day basis. Because of this, we only ever have an estimate of *R*0 in a population. An important related concept is the effective reproduction rate (abbreviated “*R*”), which is similar to *R*0 but reflects our estimate of spread when not all of the population is susceptible to infection. A good overview is here.

Herd immunity functions by reducing the number of susceptible people in the population, and is generally considered to be achieved when the proportion of immune people is high enough to push *R* under 1. We can roughly estimate the proportion of the population that needs to be immune for herd immunity (termed *Vc*) to go into effect using this equation:

*Vc* = 1 — (1 / *R0*)

For example, for measles, a common estimate of *R*0 in an urban population is around 18; thus we’d need about 95% of the population to be immune to have herd immunity. Estimates of COVID19 *R*0 have put it between 2.5 and 5, which suggests a need for between 60 and 80% of the population to develop immunity before heard immunity is achieved.

Unfortunately, in practice that simple equation doesn’t usually work. There are three significant factors to consider. First, estimating the proportion of the population that needs immunity depends on getting a good estimate of *R*0. Second, the immunity needs to be randomly distributed in the community. If there are clusters in the population that are systematically excluded from immunity, then it’s possible for the infection to overcome larger herd immunity (this is what we’re seeing with the measles outbreaks in anti-vaxxer communities). Lastly, this model depends on individuals achieving total immunity. When infection or vaccination only grants partial immunity, then we have to increase the total proportion of the population with partial immunity even further (represented as *Vcp*). This is generally calculated as

*Vcp* = *Vc*/*E*

where *E* is the proportion of people who have immunity after vaccination. To illustrate, if only 75% of people develop a strong immunity after vaccination, then for a virus with an *R*0 of 2.5 we’d need 80% of people to be vaccinated (instead of 60% if we had total immunity). Unfortunately, if the *R*0 is 5, we’d need 106% of people vaccinated, which is impossible. In general, if *E* is larger than *Vc*, then immunization won’t be effective at containing the infection. A good primer on the epidemiology of herd immunity can be found here.

Bringing this all back to COVID19, we quickly run into some thorny issues. We’re still developing estimates for *R*0 for COVID19, which means that our best estimates of *Vc* are very speculative right now. We also have evidence that suggests infection does not confer immunity, or at best only partial total immunity. This means that even if we have 100% infection, we might not achieve herd immunity. Further, if the virus evolves at a rapid pace (which it seems to be doing), it’s likely that we may develop immunity to one strain only to be susceptible to others (which is a common problem with coronaviruses in general). Lastly, immunity acquired through infection isn’t randomly distributed in the way that herd immunity requires — it naturally creates segmentation. At minimum, this would mean that we’d need to increase immunity levels substantially above a baseline estimate. Taken together, it means that hoping we will all naturally develop immunity at a level sufficient to protect the community would be a slow process that would require extremely high rates of infection, and even then might not work. It’s probably only achievable through a universal vaccination campaign with a highly effective vaccine, or a well regulated series of boosters. Thankfully, there are people working frantically to develop such tools!

As a minor aside, it is worth talking about the death toll to achieve that level of infection and thus potential immunity. As of right now (10AM on 5/6/20), the CDC is reporting 1,171,510 cases in the US. If we estimate the true infection population is 10x that amount, then that means that we’re only at about 3.5% of the US population infected. If we scale this up linearly (which will be an underestimate), then at 60–80% infection rate we’re looking at around 1–2 million deaths. These numbers also do depend on us keeping the curve flattened, which means keeping measures to reduce spread rate in place; if we remove those preventative steps then it’s likely we’ll see renewed curve growth. That’s an expensive gamble for something that might not even work.

In the meantime, we do have a second avenue of intervention. Instead of reducing *R*, we can reduce *R*0. This is what our current public health interventions do. If we identify contagious people through systematic testing and contact tracing to isolate people during contagious windows, reduce the likelihood of infection during contacts through the use of PPEs and disinfectants, and reduce the number of contact events through sheltering in place and social distancing, we can disrupt the infection transmission and reduce *R*0. If we can sustain those interventions and push *R*0 below 1 for our population, we can successfully contain and beat the virus. This is exactly what has happened in China, South Korea, New Zealand, Vietnam, Taiwan and many other countries, where the current transmission *R*0 of the virus has essentially been reduced to 0. Unfortunately, this also requires real commitment to these measures; doing them as half measures (as much of the US has) means we might reduce *R*0 but not push it below 1, or sustain it there long enough to be meaningful.

Since we’re talking countries, we should talk about Sweden, because that’s where a lot of the Herd Immunity conversation is coming from. Officially, Sweden isn’t trying to do herd immunity, at least according to their foreign minister. They’re gambling on people electively reducing contact, and that their healthcare system (which is much more robust than ours) will be able to identify and isolate infections before they spread. They’re also gambling that having a generally healthier population will grant some protection. So far, the data doesn’t look good. Let’s compare Sweden to Georgia (as of 10AM on 5/6/20), since they have similar populations (about 10M). In GA, we have around 1300 deaths so far; Sweden is just under 3000. Interestingly, Sweden has detected fewer cases than GA has (23K to 29K); this suggests that their monitoring hasn’t been particularly effective. If we look at Case Fatality Rates, Sweden is at around 12%, while GA is only around 4% (we should treat this with some skepticism; we’re clearly under-counting in both places). Given that GA’s population has a much higher rate of “underlying conditions”, this discrepancy is alarming. Sweden also has the 7th highest death toll per capita, and has one of the fastest growing fatality rates in Europe. It’s not a winning strategy.