The dangerous myth that Sweden achieved herd immunity

(Note: Bracketed citations correspond to a list of references here)

The COVID-19 pandemic continues, with public health responses varying between countries [1]. Some commentators claim Sweden’s response resulted in herd immunity that protects their population [2]. This article instead argues that Sweden, and regions within it, almost certainly did not reach the herd immunity threshold. Section 6 summarizes some reasons why this is so, while sections 1 to 5 discuss the reasons and their implications in more detail.

I know of no epidemiologist, immunologist, or other expert who claims Sweden achieved herd immunity. They instead note the danger of pursuing herd immunity without a vaccine [3]. So to better understand why various experts hold this view, let’s first start with what herd immunity is and why it’s important.

Section 1 : A basic introduction to herd immunity

SARS-CoV-2, the virus that causes the disease COVID-19, infects a susceptible person and uses them to infect another susceptible person. Some people may naturally resist the virus. Or they resist the virus because SARS-CoV-2 previously infected them and their immune system then adapted to it. Resistant people’s bodies clear the virus, so resistant people fail to pass SARS-CoV-2 on to susceptible people. Herd immunity arises when so many people become resistant that the virus has trouble reaching susceptible people to infect; this protects susceptible people. Hence the immunity of the resistant herd indirectly protects its susceptible members. One can achieve herd immunity with a vaccine containing components of SARS-CoV-2, or by allowing SARS-CoV-2 to infect people [4]. Figure 1 below depicts the overall process:

Figure 1: {Panel A} A very basic model of infection, in which susceptible people (S) become infected (I), and then eventually resistant to infection (R) as time progresses. {Panel B} The infection transmits more readily in a “naïve” population that lacks prior exposure or resistance to the virus, in contrast to a population with herd immunity and a greater proportion of resistant people. The color-coding for panels A and B is the same [5].
Authors of the figure: https://www.sciencedirect.com/science/article/pii/S1074761320301709

We can put this in slightly more technical terms using the concept of a reproduction number (R). R basically represents how contagious the virus is in a given circumstance. At R = 1, one infected person infects 1 new person on average. At R = 2, one infected person infects 2 new people on average. And so on. A larger initial R implies more people need to be infected or vaccinated in order for herd immunity to occur; in other words: a higher initial R implies a higher herd immunity threshold (HIT). Once R falls below 1 with herd immunity, the viral outbreak continues into its descending phase as the number of new infections fails to fully replace those who recovered from infection.

The above discussion glosses over some details, such as the difference between the basic reproduction number (R0) and the effective reproduction number (Rt). But the points above should suffice for this article. For those who want further details, please consult the reference list [6].

Section 2 : The ‘multiple peaks problem’ for herd immunity

Some commentators infer that Sweden as a whole, and/or particular regions of Sweden, reached HIT since new COVID-19 cases/day, hospitalizations/day, and deaths/day decreased [7]. But a problem arises for this inference, as illustrated by the following discussion of an outbreak of hepatitis E virus:

“If significant herd immunity developed following initial major water supply contamination, a multipeaked and/or prolonged epidemic would not be expected to occur [8].”

So multiple infection peaks conflict with herd immunity, since herd immunity should protect against second waves of infection [9]. Conceptually, this makes sense: immune protection causes a continual decline in new infections/day, as per R < 1. In contrast, a second peak implies there was not a continual decline in infections/day because another increase in infections/day caused the second peak. That entails R > 1, with an absence of herd immunity. This increase in new infections/day elevates cases/day, which then later increases deaths/day because it often takes time for COVID-19 patients to die [10].

Herd immunity therefore comes with only one peak in deaths/day. Yet Sweden shows multiple peaks in COVID-19 deaths/day on or after the late April time-period by which commentators claim [11] Sweden achieved herd immunity. Figure 2 thus shows at least three peaks centered at:
- ~April 25
- ~May 10
- ~May 30

If these peaks represent data artifacts, then this undermines the credibility of the data commentators use to claim Sweden reached HIT. But if these instead represent real underlying changes in COVID-19 deaths, then the peaks in death/day should be preceded by peaks in new cases/day and in the proportion of people who test positive, since many COVID-19 patients die weeks after the onset of symptoms [12]. Both sets of predicted peaks occurred, though they are more pronounced in new COVID cases/day. So figures 3 and 4 show at least three peaks centered at:
- ~April 11/12
- ~April 24/25
- ~May 12/13

Figure 2: 7-day moving average for COVID-19 deaths per day per million people in Sweden [13]. Alternative data analyses are available [14]. The time-frame of March 1st to July 5th was selected to match figure 4.
Authors of the figure: http://archive.is/wwfcA

Figure 3: 7-day moving average for new COVID-19 cases per day per million people in Sweden [15]. An alternative data analysis is available [16]. The time-frame of March 1st to July 5th was selected to match figure 4. Tests per day increased in June with a change in testing protocol [17]; this likely accounts for the spike in cases/day in June.
Authors of the figure: http://archive.is/n9bDW

Figure 4: 7-day moving average for percentage of people who test positive per day per million people in Sweden [18]. Tests per day increased in June with a change in testing protocol [19]; this likely accounts for the spike in proportion of positive people per day in June.
Authors of the figure: http://archive.is/jyShH

Section 3 : Resolving the ‘multiple peaks problem’

Unfortunately, some commentators miss the ‘multiple peaks problem’ and instead infer herd immunity occurred because of a decrease in COVID deaths/day or new cases/day [20]. As Nic Lewis states:

“Conclusions
Notwithstanding that a month ago antibodies were only detected in 6.3% of the Swedish population, the declining death rate since mid-May strongly suggests that the herd immunity threshold had been surpassed in the three largest regions, and in Sweden as a whole, by the end of April [21].”

In reaching his conclusions on herd immunity, Lewis applies [22] research in a way objected to by one of the co-authors of that research [23]. He also uses graphs with lower temporal resolution, which obscures any multiple peaks in Sweden’s data. This allows him to say that there is an “almost monotonic decrease in deaths in [the] Stockholm region [24].” Yet as previously shown, when one looks at Sweden as a whole, COVID-19 deaths/day decreased in a non-monotonic fashion with multiple peaks and in a manner inconsistent with herd immunity. So one cannot infer a region reached the herd immunity threshold just because new COVID-19 cases/day, hospitalizations/day, and deaths/day decreased, since factors other than herd immunity could better explain those decreases.

Factors such as changes in behavior can cause multiple peaks [25]. For example, suppose people engage in infection-preventing behavior in response to increasing COVID-19 deaths/day. This behavior decreases deaths/day; people then relapse on their infection-preventing behavior as they become aware of the decreasing deaths/day. Complacency begets a relapse. Their relapse again increases new infections/day and deaths/day because the virus can still reach people with susceptible immune systems; i.e. because HIT was not reached. This increase in deaths/day again causes people to engage in infection-preventing behavior, which starts another decrease in deaths/day. Concern begets prevention.

This increasing and decreasing pattern results in another peak [26]. Figure 5 models this fluctuation as people change their behavior in virtue of their short-term and/or long-term awareness of shifts in deaths/day:

Figure 5: Modeled deaths/day as people change their behavior due to short-term and/or long-term awareness COVID-19 deaths, as deaths cross a critical cumulative fatality level represented by NDc. The dashed line represents short-term social distancing alone, and the population size is N = 10 million people [27]. Note that Sweden’s population is ~10 million, so the y-axis values of figure 5 can be divided by 10 to match the y-axis values of figure 2.
Authors of the figure: https://web.archive.org/web/20200701170752/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7273247/

Figure 5 thus illustrates how changes in behavior can result in multiple peaks and decreasing deaths/day in the absence of herd immunity. As the authors of figure 5 note:

“These early onset peak rates should arise not because of herd immunity but because of changes in behavior. […]
The peaks occur at levels of infection far from that associated with herd immunity [28].”

Though multiple peaks imply the absence of herd immunity, the converse is not true since, for instance, stringent interventions such as shelter-in-place orders could make people’s infection-preventing behavior less sensitive to changes in deaths/day. So a one peak, monotonic decrease in deaths/day could occur even in the absence of herd immunity [29], as per figure 5.

Section 4 : Non-herd-immunity factors limited COVID-19 deaths

Along with multiple peaks, the proportion of COVID-19 deaths per infection did not decrease with relatively higher rates of infection, contrary to what one would expect if herd immunity limited deaths [30]. And different European countries plateaued at different levels of COVID deaths per capita [31], with these levels being related more to the nature of their public policy interventions than to immunologic factors tied to herd immunity [32]. Thus, shelter-in-place orders, variations in personal behavior, etc. decrease COVID-19 deaths/day and new cases/day at infection rates far below HIT [33].

Commentators likely confuse the effect of these factors with that of herd immunity, despite the differences between them. For instance, immune-susceptible people can roam freely in the end-stages of herd immunity. A classic example of this is children who cannot be immunized for medical reasons; vaccine-induced herd immunity allows them to attend school. But if this immunity wanes due to low vaccination rates [34], then these children need other forms of protection, such as isolation from the large concentrations of people present in a school. Yet Lewis claims many of Sweden’s COVID-19 deaths result from the government not limiting SARS-CoV-2 infections in care facilities [35]; i.e. the immune-susceptible could not roam freely and needed isolation.

More SARS-CoV-2 infections community-wide increases the chances that SARS-CoV-2 will infect those in a community’s care facility [36], likely via infected facility staff [37]. So shelter-in-place orders can limit infections in these care facilities by, for example, limiting infection risk for facility staff in densely populated areas and for those living with facility staff [38]. These orders, along with other public health interventions and behavior changes [39], would also help prevent large concentrations of people that allow SAR-CoV-2 to infect most of those present [40]. So factors such as stay-at-home orders, prohibiting outside visitors to care facilities / isolation, and behavioral changes protected immune-susceptible people [41], not herd immunity.

Evidence so far points to a HIT of >50% for both natural infection and vaccine-induced herd immunity [42], but some experts speculate HIT lies between ~40% to ~60% [43]. This is on the lower end of classical calculations of HIT based on R [44], but consistent with recent research on factors that can lower HIT [45]. To my knowledge, no country surpassed a >50% threshold for the proportion of people infected, though a number of regions suffered infection rates higher and more divergent than one would expect if a very low HIT limited the infection rate [46].

Sweden has not even achieved the more modest threshold of >40%, nor has any region within it; Sweden is not even halfway there [47]. As noted in mid-June by Sweden’s state epidemiologist: their trends toward immunity have been “surprisingly slow” and it remains difficult for them to explain why [48]. This contrasts with his more optimistic tone in April [49], at the time commentators claimed Sweden achieved herd immunity [50].

(Technical note: Some might object that Sweden came much closer to HIT than studies show, since antibody-based studies under-estimate infection rates and fail to capture T-cell-based immunity [51]. But this response pays insufficient attention to the expected/predicted rate of true negatives for these antibody tests, whether the test’s sensitivity was stated, and the risk that T cell responses sometimes worsen COVID-19 instead of providing protective immunity [52]. The research in question also would not bring Sweden close to a >40% threshold, even if one grants their stated proportion of antibody-negative patients [53].)

Section 5 : Deadly implications of chasing non-vaccine-induced herd immunity

In claiming a low HIT of ~17% or less for Sweden, commentators sidestep factors that can increase HIT, such as SARS-CoV-2 better evading the immune system [54]. Their claim also conflicts with evidence from prior pathogens [55]. Take the seasonal flu, another respiratory viral condition that kills elderly people more than younger people [56]. A low HIT for SARS-CoV-2 implies HIT for seasonal flu lies below the mainstream prediction of ~16% to ~27% [57]. Yet in reality, HIT for flu remains high enough that medical professionals vaccinate numerous people for influenza instead of pursuing herd immunity via natural infection [58].

So it is untenable to reach herd immunity for SARS-CoV-2 rapidly at a lower threshold, especially when SARS-CoV-2 is more contagious than seasonal influenza (i.e. has a higher initial R) [59], kills >10 times more of those it infects [60], and kills more people overall [61], even with all the extraordinary steps taken to limit SAR-CoV-2’s impact. A large number of COVID-19 deaths would therefore occur in a non-vaccine-mediated attempt to achieve SARS-CoV-2 herd immunity [62]. Yet some non-expert commentators claim Sweden achieved herd immunity [63]. One might thus expect a relatively large number of COVID-19 deaths in Sweden:

Figure 6: COVID-19 deaths per capita in Europe. Sweden is the dark red regional outlier in the top middle of the page [64], with one of the 5 highest deaths per capita among 40+ European states (excluding microstates) [65].
With respect to the 4 states with higher deaths per capita than Sweden [66]: Belgium counts COVID-19 deaths differently from other states, increasing Belgium’s total count [67]. Spain and Italy were the first states hit hard by the pandemic [68]; they therefore could not learn from the experience of other European nations. Finally, the United Kingdom flirted with Sweden’s so-called ‘herd immunity’ strategy for a time, before moving to a poorly-enforced lockdown [69]. Outside of those 4 states, the Netherlands [70] also followed Sweden’s strategy for a while, before implementing a lax lockdown [71]. And Belarus has yet to implement a lockdown [72], though they remain in the early phase of their outbreak, as their COVID-19 deaths/day continue to increase [73].
Authors of the figure: http://archive.is/fmsLP

So Sweden’s strategy led to more COVID-19 deaths per capita in comparison to its neighbors that promptly locked down / gave shelter-in-place requirements [74]. Some defenders of Sweden’s strategy avoid this point by not comparing Sweden’s COVID-19 deaths per capita to that of its immediate neighbors [75]. Other failed defenses of a herd-immunity-based strategy include:
- under-estimating the fatality rate for SARS-CoV-2 infection [76]
- noting COVID-19 deaths in care facilities [77], while ignoring how allowing for community-wide infection to achieve herd immunity increases the risk of infection in care facilities [78]

Nor does a herd-immunity-based strategy save lives by avoiding substantial economic losses [79]. After all, COVID-19 deaths themselves harm the economy. Other countries may also block travel to, and incoming from, a state allowing high rates of active infection, further harming the economy of said state [80].

The aforementioned points tie into why some non-expert commentators incorrectly claim Sweden achieved herd immunity [81]: they want to show a country successfully addressed COVID-19 without the shelter-in-place orders / lockdowns these commentators oppose for political reasons [82]. This illustrates the risk of (intentional or unintentional) ideologically-motivated, non-expert distortions of science [83]. Given that, I’ll conclude this section with comments related to epistemic trespassing [84] into a field in which one lacks expertise:

“AS A STATISTICIAN, I respect science expertise because I need it to do my job right. In the early days of the pandemic, I saw debate develop between those advocating we listen to experts and those who felt we should listen to the data. This is a false dichotomy […]
This false dichotomy was concerning to me because analyzing data without scientific expertise is dangerous. Analysis needs to be grounded in real world experience (derived from experiments) of what is plausible. Without this, we can be worse off for having looked at the data [from Kareem Carr] [85].”

“How to be Curious Instead of Contrarian About COVID-19
[…]
Lesson 4: Form Meaningful Prior Beliefs with a Thorough Literature Review [from Rex Douglass] [86]”

“I’m constantly amazed at Nic Lewis’ ability to do paradigm shifting work in so many different fields and with little chance to thoroughly [familiarize] himself with the finer details of the topic [from Ken Rice] [87].”

(See the end-note [88] for further discussion of problems with the ‘Sweden achieved herd immunity’ hypothesis. And in case people would like to know my pertinent expertise: I am an immunologist.)

Section 6 : Summary

Sweden, and the regions within it, did not achieve herd immunity for at least the following reasons:

1. multiple peaks occurred in Sweden’s COVID-19 deaths/day and new cases/day, when only one peak should occur if Sweden achieved herd immunity
2. various factors kept the threshold above 40%, and likely above 50%, which remains higher than Sweden’s observed infection rate
3. shelter-in-place orders, changes in behavior, physical isolation of those at risk, etc. explain observed decreases in deaths/day better than does herd immunity
4. infection rates in some areas exceeded what a low threshold would predict
5. deaths per capita and infection rates plateaued at different levels in different countries, with no clear relationship to herd-immunity-relevant factors
6. deaths per infection did not decrease at higher rates of infection
7. a low threshold conflicts with evidence from prior pathogen outbreaks

Pursuing herd immunity to SARS-CoV-2 without a vaccine substantially increases COVID-19 deaths.