The Problems with the “Natural” Herd Immunity Solution to the Covid-19 Epidemic

Par Luís Santos-Pinto et José Mata

Now that the lockdown is softening in Switzerland, it is tempting to think that we can go back to our normal lives. Most of us are tired of being at home all the time, and many people have been suffering from not being able to earn regular income. The deadly example of San Francisco 102 years ago, when many residents refused to accept keeping protective measures against the Spanish flu, shows the risks of euphoria following the end of lockdown. 

The risks are exacerbated because there are those who argued that a “natural” herd immunity strategy is the best approach to the covid-19 epidemic. Herd immunity occurs when a significant proportion of the population (or the herd) are able to resist a disease by the action of antibodies or sensitized white blood cells (e.g. due to a vaccine), resulting in protection for susceptible (e.g. unvaccinated) individuals. As with any other infectious disease, there are two ways of achieving herd immunity: a large proportion of the population either gets a protective vaccine (herd immunity by vaccination) or becomes infected and develops immunity (natural herd immunity).

Proponents of the natural herd immunity have put great weight in the advantages of this strategy, which revolve around causing minimal disturbance to normal economic activity. As a consequence of keeping normal life, job losses and reduction in income would be minimized, and productive capacity would not be destroyed. Much lower weight is placed on the disadvantage of such strategy, namely on its potential toll in terms of human lives. The strategy to which most countries have now adhered is different, and was coined as “the hammer and the dance” by Puyeo (2020). This strategy consists in applying harsh social distancing measures to prevent the spread of covid-19 (“the hammer”), and keeping the virus under control using testing and tracing until eventually a vaccine is found (“the dance”). 

The choice between these two strategies involves a hard trade-off, mostly between economic activity and human lives. We do not want to minimize the impact of diminishing economic activity. Losing income may have severe costs, in particular to those who have weaker social protection nets. Destroying productive capacity, namely by having firms going out of business, may extend considerably the period of economic hardship, as equally efficient new firms will not immediately appear after the disease is controlled. If the severity of the disease is low, the disadvantages are slim, and there are good reasons to let the epidemic follow its natural course. However, and while proponents of the natural herd immunity strategy have presumed that these costs are low, the truth is that covid-19 and its effects are still largely unknown. 

When there is great uncertainty about one of the alternative strategies, option theory tells us that there is value in waiting to have the uncertainty resolved before committing to one of the alternatives, in particular if that choice has irreversible consequences and if the level of uncertainty is high. We consider six key uncertainties associated with the covid-19 epidemic:

1 – The uncertainty about the basic reproduction number

2 – The uncertainty about the infection fatality rate

3 – The uncertainty about the infection injury rate

4 – The uncertainty about the body’s immune response

5 – The uncertainty about covid-19 mutations

6 – The uncertainty about finding treatments and a vaccine

This article discusses what we know now about these six key uncertainties and how our knowledge has progressed since the beginning of the crisis. Time plays a critical role in getting to know better the true consequences of the virus and in giving us more information to make informed decisions.

The Option Value of “the Hammer and the Dance”

Option theory was developed to analyze financial and real investments (Dixit and Pindyck, 1994), but its basic principle can be illustrated with facts of common life. Consider two youngsters who are looking to start a family, meet each other, and are pleased with their first impressions. Should they move together right away? While separations are possible, they typically entail emotional and material costs that are not negligible and thus there is some component of irreversibility in the decision of moving together. Most people would advise against moving together immediately and would advise instead that they date for some time, since dating would enable them to get more information about each other and about their potential fit. 

We can think of the choice between natural herd immunity and “the hammer and the dance” in these same terms. Even if countries can revert from a natural herd immunity strategy, the fatalities and injuries associated with it are irreversible. However, if a country chooses “the hammer and the dance”, then it waits for more information about the covid-19 before making a decision. The option value of waiting can be significant given the extremely high level of uncertainty of the covid-19 epidemic, as we shall see next. 

Uncertainty about the Basic Reproduction Number

The basic reproduction number (R₀) is the average number of secondary infections produced by a typical case of an infection in a population where everyone is susceptible and there are no containment measures in place. The R₀ tells us two important things about an epidemic. First, the probability the virus spreads through the population. Second, it gives us the herd immunity threshold (hit), that is, the proportion of the population that needs to be immune such that the spread of the virus is limited and the population is protected against new infections. 

The effective reproductive number (R_t) is the average number of secondary cases per infectious case in a population at each moment t when the population consists of both susceptible and immune individuals. If R_t >1, the number of cases will increase over time. Where R_t = 1, the disease is endemic, and where R_t < 1 there will be a decline in the number of cases. The R_t can be estimated by the product of the proportion of the population that is susceptible at time t, s_t, and the R₀ (note that s_t = 1 – p_t, where p_t is the proportion of the population that is immune at time t). That is: R_t = s_t x R₀ = (1-p_t) x R₀. Hence, to get R_t below 1 one must have (1-p_t) x R₀ < 1 or, equivalently, p_t > hit = 1 – 1/R₀. 

The value hit = 1 – 1/R₀ is the herd immunity threshold. If this threshold is reached, for example, through natural herd immunity, then each case leads to a single new case (R_t = 1) and the infection will become stable within the population. 

Typically, at the start of a new epidemic, there is a lot of uncertainty about the R₀. If we do not know the exact R₀ of covid-19, we cannot tell what proportion of the population needs to become infected and immune to reach natural herd immunity.

Indeed, in covid-19’s case, the R₀ in most countries seems to be a number between 2 and 4 (Hausmann, 2020). If each infected person infects an average of three others (R₀ = 3), the herd immunity threshold is 66.6%, and two-thirds of the population needs to become infected and immune to attain natural herd immunity.  However, if each infected person infects an average of four others (R₀ = 4), the herd immunity threshold is 75%, and three-fourths of the population need to become infected and immune to reach natural herd immunity. Should the uncertainty about the R₀ concern us? Yes, since different values for R₀ can lead to very different estimates for the number of fatalities and injuries associated with a natural herd immunity strategy. This will become clear through an example below.

Uncertainty about the Infection Fatality Rate

More than four months have passed since the covid-19 epidemic started and there is still plenty of uncertainty about the infection fatality rate (IFR). The IFR is the ratio of the number of deaths to the number of actual infections with a disease. The IFR tells us the severity of a disease in terms of the number of deaths of infected individuals. The IFR of the seasonal flu is about 0.05%. We still do not know if the IFR of covid-19 is 0.1% (2 times more deadly than the seasonal flu), 0.5% (10 times more deadly), 1% (20 times more deadly), or 5% (100 times more deadly).

Different values of the IFR lead to drastically different estimates for the number of fatalities associated with a natural herd immunity strategy. To illustrate this point, consider the case of Switzerland with a population of approximately 8.655.000 individuals. We do not yet know the basic reproduction number of covid-19 in Switzerland, but let us assume it is 3, that is, each person infects an average of three others. The cumulative number of fatalities in Switzerland is currently 1790. With a R₀ of 3 and IFRs of 0.1%, 0.5%, 1%, and 5% the natural herd immunity strategy would lead to 5770, 28850, 57700, and 288500 total fatalities, respectively. Hence, under a natural herd immunity strategy, even seemingly low IFRs can translate into shockingly large death tolls given that the virus spreads through a major portion of the population. Of course, fatalities would be even higher if the R₀ is greater than 3. With a R₀ of 4 and IFRs of 0.1%, 0.5%, 1%, and 5% the natural herd immunity strategy leads to at least 6491, 32456, 64912, and 324562 total fatalities, respectively. 

To know the IFR one needs to perform serological tests to a representative random sample of the Swiss population. There are different types of serological tests in the market but they have yet to be compared in terms of their accuracy (false positive and false negative rates) before we know which ones can be trusted. However, even without performing serological tests, it is possible to find lower and upper bounds for the IFR. These bounds allow us to understand how much we don’t know about the IFR. When the bounds are far apart, there is large uncertainty about the IFR. In contrast, when the bounds are close together, there is little uncertainty about the IFR.  

The mortality rate (MR) provides a lower bound for the IFR. The MR is the ratio of the number of deaths due to covid-19 to the population in a given country. The MR is a lower bound for the IFR because most people in the population are not infected. The all-in case fatality rate (all-in CFR) and the closed case fatality rate (closed CFR) provide an upper bound interval for the IFR. The all-in CFR is the ratio of the number of deaths due to covid-19 to the number of confirmed cases of covid-19 (the sum of deaths, recovered, and active cases). The closed CFR is the ratio of the number of deaths due to covid-19 to the number of closed cases of covid-19 (the sum of deaths and recovered cases). The all-in CFR and the closed CFR provide an upper bound interval for the IFR because the actual number of infected individuals is higher than the number of confirmed cases (a large number of the infected are asymptomatic and therefore do not get tested). 

What do we know about the IFR in Switzerland in the early stages of the epidemic? On 13^th of March 2020, the day the social distancing measures were announced, the MR, the all-in CFR, and the closed CFR were 0.0001%, 0.97% and 73.3%, respectively.  Hence, on the 13^th of March 20202, the IFR was greater than 0.0001% but smaller than a value contained in the interval [0.97%, 73.3%]. What do we know now about the IFR in Switzerland? Today, the MR, the all-in CFR, and the closed CFR are 0.02%, 5.8%, and 6.4% respectively. Hence, today we know that the IFR is greater than 0.02% but smaller than a value contained in the interval [5.8%, 6.4%]. 

As we can see, the time elapsed between the 13^th of March and today led to a significant reduction in the uncertainty about the IFR in Switzerland. However, and shocking as that may be, we are still not able to rule out the possibility that covid-19 is 100 times more deadly than the seasonal flu.

Uncertainty about the Infection Injury Rate

Imagine you are a general who is planning to either make war or sign a peace treaty. You know that if you make war, 1 in 100 soldiers will die and for each dead soldier there will be 10 seriously injured. This is a very different scenario than, let’s say, one where 1 in 100 soldiers will die and for each dead soldier there are 100 seriously injured. Even though the death rates are the same in both scenarios, the injury rate in the second scenario is 10 times higher than in the first. 

People who have been exposed to covid-19 and who recover are not necessarily back to good health. In critical cases who later recover, the covid-19 can cause irreversible damages to the lungs and to other organs (Ferreira, 2020). We do not yet know the proportion of the population that will suffer serious injury to their health after exposure and survival to covid-19, but an increase in such a proportion has consequences in both the private and social domains. Unhealthy individuals will become less productive and will earn less income for the rest of their working lives, and they tend to be heavy users of social insurance programs.

Uncertainty about the Body’s Immune Response

We still do not know if an infected person develops enough defenses that make him or her immune to catching covid-19 once again (Iwasaki, 2020). If there is no natural immunity (or if natural immunity lasts very little time), then the herd immunity strategy is useless. As Bergstrom and Dean (2020) point out: “For this to work, prior infection has to confer immunity against future infection. While hopeful, scientists are not yet certain that this is the case, nor do they know how long this immunity might last. The virus was discovered only a few months ago.”

Uncertainty about Covid-19 Mutations

The natural herd immunity strategy assumes that the covid-19 does not mutate much. If this is the case, the epidemic dies out when the herd immunity threshold is reached. However, we do not know if the covid-19 mutates much or not. Moreover, we know that the more people are infected, the more opportunities covid-19 has to mutate.

Uncertainty about Finding Treatments and a Vaccine

Keeping social distancing measures in place might also buy us time to develop treatments and a vaccine to covid-19. Proponents of a natural herd immunity strategy assume that herd immunity by vaccination is not viable. However, this is not necessarily the case. Many countries are currently pouring funds into developing a vaccine for covid-19. Time is needed to develop, test, manufacture, and distribute a vaccine. 

The National Health Service’s Capacity Constraint

Much has already been said on this issue but it is important to recall it. If the IFR is high and consequences of the disease are serious, the natural herd immunity strategy leads to a potentially large number of critical hospitalization cases. As the health system has a maximum capacity of people and material, occupying a significant part of it with the covid-19 will reduce the ability to treat other diseases and to increased deaths from causes other than covid-19. 

In addition to reducing the capacity to treat patients with other diseases, there is another side effect of an overstretched health system. It has been observed in some countries that people with other severe diseases avoided seeking help from the health system for fear of being infected in hospitals. The more the health system is overwhelmed with the covid-19, the more likely is this effect to hold.

Conclusion

In an interview to CNN released just before we finished writing this article, Dr. Anthony Fauci asked the following question: “How many deaths and how much suffering are you willing to accept to get back to what you want to be some form of normality sooner rather than later?” Unless you are prepared to accept a very high number of casualties, it is unlikely that anyone can currently give you a go. 

We now know much more about covid-19 than we knew at the start of the epidemic. However, there are still many things we need to find out (Avery et al., 2020; Flaxman et al., 2020; Kresge, 2020; Silver, 2020; Wu and MacCann, 2020). We need to figure out what is the basic reproduction number of covid-19. We need to perform an antibody test to a representative sample of the population to determine the infection fatality rate. We need to use hospitalization records to figure out the infection injury rate. We also need to find out whether individuals exposed to covid-19 develop natural immunity or not. 

Choosing the best strategy to respond to the covid-19 epidemic implies taking into account not only the costs and benefits associated with each alternative but also the option value of waiting. This value is bound to be large given the high uncertainty we face. Proponents of the natural herd immunity strategy overlook six key uncertainties associated with the covid-19 but also the implications of the national health service’s capacity constraint. Keeping social distancing measures in place that will help the uncertainty to be resolved is our best course of action for now. But at the same time, we need to invest decisively in collecting data that will provide us information on the different sources of uncertainty identified above.

Luís Santos-Pinto est Professeur ordinaire à la Faculté des HEC de l’Université de Lausanne. Son principal domaine de recherche est la théorie microéconomique appliquée. Il étudie les liens entre l’information, la cognition, le jugement et le comportement économique.

José Mata est Professeur ordinaire et Directeur du Département de stratégie à la Faculté des HEC de l’Université de Lausanne. Il s’intéresse à la dynamique des marchés et aux stratégies des entreprises.