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Home / Publications / Research / Economic Brief / 2021

Economic Brief
May 2021, No. 21-16

Who Should Get Vaccines First?
Article by: Joshua Weiss and Nikhil Vellodi

We study optimal vaccination policies using a novel theoretical framework. We
characterize the optimal vaccine allocation scheme in our model, which entails
giving the highest priority to people with intermediate vulnerability and giving
greater weight to potential exposure rather than vulnerability. Numerical results
demonstrate that this approach performs signi cantly better than commonly
considered strategies, in particular prioritizing only people who are the most
vulnerable to severe illness.

Vaccination policies are crucial to eradicating pandemics. Given the scarcity of supply and
the urgent need for rollout, optimizing vaccine allocation is of paramount importance.
Prevailing views revolve around two key considerations: vulnerability risk and transmission
Sensible arguments can be made for allocating the vaccine to those most likely to su er
severe symptoms, as well as to those most likely to contract and spread the disease. Thus
far, however, policymakers and researchers have devoted little attention to the role that
incentives and behavior play in designing optimal vaccine policy.1
A recent report by the World Health Organization documents the growing importance and
policy relevance of various behavioral incentives under the heading "lockdown fatigue,"
referring to the rejection of mandatory isolation requirements.2 Prudent policy design
should account for human behavior rather than establishing rules under the assumption of
full compliance.
A burgeoning literature aims to incorporate behavior into standard susceptible-infectedrecovered (SIR) dynamic epidemiological models, primarily to study the evolution of
contagion rates.3 These and other similarly quantitative models o er a strong methodology
for generating robust predictions.
However, they quickly become analytically unwieldy when combined with other
considerations, such as individuals who vary across multiple dimensions. These models can
be used to compare particular policies but are not well-suited to characterizing the optimal
vaccine prioritization scheme in complex settings.4 This complexity is necessary to ascertain
the relative importance of vulnerability risk versus transmission risk in vaccine prioritization

Vulnerability and Transmission Risk
That's why we take a di erent, complementary approach in a recent working paper.5 We
develop a simple, tractable model that abstracts from the dynamic considerations found in
SIR models but allows for a rich level of vulnerability risk and transmission risk
heterogeneity across individuals, as well as behavior that responds to the state of the
pandemic. Throughout the analysis, an individual's overall risk of severe disease is a
product of vulnerability and exposure.
Vulnerability refers to a person's likelihood of experiencing severe symptoms or death if
infected, which, in the model, is due solely to factors beyond the individual's control within
the timeframe of the pandemic. In the real world, vulnerability is likely a function of age or
underlying health conditions.

Exposure refers to the frequency of interactions with others, during which an individual can
contract or spread the disease. Unlike vulnerability, exposure is a function of behavior as
well as factors beyond the individual's control. This assumption captures the idea that some
people have jobs, social circles or living conditions that involve more frequent contact with
others, but that they can take costly actions — such as working from home or changing
their living circumstances — to avoid those interactions.
We characterize the optimal allocation of vaccines and provide useful qualitative insights to
guide real-world vaccination policy. The baseline analysis produces two main ndings:
First, among individuals with the same level of overall risk, it is better to vaccinate those
whose risk is due to a high level of exposure rather than a high level of vulnerability.
Second, if optimal lockdown policies are not implemented or followed, it is best to give
special priority to individuals who tend to interact more than is socially optimal.
The model also provides insight into when it is better to vaccinate with the goal of herd
immunity rather than directly protecting particular individuals.

A Tractable Model of a Pandemic
We develop a model with a large number of individuals indexed by both their probability of
potential exposure to others (entering and expanding the interaction pool) and their
probability of su ering severe reactions to the disease if they become infected. A person's
overall risk of a severe reaction is the product of the two probabilities multiplied by a term
common to all people that re ects the aggregate state of the pandemic.
The larger the number of individuals in the interaction pool, the higher the probability of
contracting the disease in the pool. As a consequence, holding vulnerability xed, an
individual with a higher exposure not only faces a higher risk of an adverse outcome but
also exerts a greater negative externality on others by increasing the size of the interaction
Finally, an individual may self-isolate by paying a cost to avoid interactions. We impose that
the cost of self-isolation is higher for people with a greater probability of potential
exposure. It follows that, holding vulnerability xed, people with a higher exposure face a
greater burden from the pandemic because they must choose between a greater risk of
infection and a higher cost of self-isolation. This assumption captures the notion that those
who tend to interact more during normal times also face a higher cost of avoiding others
during the pandemic.
We take as given a xed quantity of vaccines that yield full protection from infection and
asymptomatic spread, and ask: How should a policymaker allocate vaccines based on
individuals' exposure risk and vulnerability risk to minimize the total costs of infection and

self-isolation? In the primary extension of the model, we also allow the policymaker to
choose which individuals will isolate, which we refer to as a mandatory lockdown policy.

Our baseline analysis displays three striking features. First, people with intermediate
vulnerability are vaccinated more than those who are either more or less vulnerable. Such
individuals interact more than is socially optimal, so they are particularly costly to society
when unvaccinated. Indeed, it is always optimal to rst vaccinate these people when
supplies are limited.
Second, among those not self-isolating, the optimal policy exhibits an exposure premium:
Vaccination is not based on overall risk. Instead, greater weight is given to exposure than
vulnerability. More speci cally, holding overall risk xed, it is better to vaccinate those
whose risk is due to a high level of exposure than due to a high level of vulnerability. This
feature re ects the social value of vaccinating individuals who tend to infect others.
Third, among those in self-isolation, the policy depends only on exposure, not on
vulnerability. Self-isolating individuals are vaccinated if their exposure, and thus their cost
of self-isolation, is su ciently high.
The latter two properties reveal two di erent ways that individuals' exposure is more
relevant for vaccine allocation than their vulnerability. For those who self-isolate, their
behavior eliminates the importance of di erences in vulnerability, yet the cost of this
behavior goes up along with their potential frequency of interaction. For those who do not
self-isolate, exposure and vulnerability contribute equally to their private overall risk, but
only their exposure contributes to the risk they impose on others.
We also characterize the optimal allocation of vaccines when the optimal mandatory
lockdown policy is in place. This yields two insights into the distortions that private
incentives concerning isolation entail. First, for those with either high or low vulnerability,
social and private incentives agree on whether self-isolation is worth the cost. However,
social incentives imply that those with intermediate vulnerability should isolate, while
private incentives — which do not include the risk of infecting others — make self-isolation
seem too costly.
Second, the value of taking into account spillovers when vaccinating — the driving force
behind the exposure premium and giving priority to those with intermediate vulnerability
— is low when the optimal mandatory lockdown policy is not implemented and there are
many individuals who are indi erent or nearly indi erent between self-isolating and
interacting. As high-interaction individuals are vaccinated and the risk of transmission falls,
people who were self-isolating may decide it is now safe enough to interact. If these newly

interacting individuals are not considering (or are not incentivized to consider) their e ect
on others, then this decrease in self-isolation is costly to society and undoes the initial
decrease in infection rates.

Comparing Optimal and Simple Vaccination Strategies
In addition to these theoretical ndings, we perform various numerical exercises in part to
compare the optimal policy to commonly considered simple strategies, such as:
Policies that vaccinate only the most vulnerable
Policies that vaccinate only the most interactive
Policies that vaccinate according to overall risk
A consistent nding is that policies that vaccinate only the most vulnerable perform
signi cantly worse compared to other commonly considered strategies, as well as to the
optimal policy. This performance gap is largest when vaccine supply is heavily constrained
or the disease is particularly contagious or deadly. In those cases, such policies end up
targeting only individuals in isolation and generate no spillovers.
This result is particularly signi cant because many countries implement such policies at the
start of a vaccine rollout, precisely when supply is most limited. Importantly, in the optimal
policy, some of the most vulnerable remain unvaccinated, but they still bene t from the
spillovers generated by focusing vaccinations on those who interact frequently.

Qualitative Guidelines for Vaccination Policy
Although our model abstracts from important quantitative considerations, it provides
qualitative insights into the optimal vaccination prioritization scheme. First, people's overall
risk is the product of their vulnerability and their frequency of interaction, but only the
latter puts others at risk. Therefore, holding overall risk xed, vaccinations should target
those who are more likely to expose others. Second, self-isolation mitigates the importance
of di erences in vulnerability. Among those who avoid interaction, preference should be
given to individuals whose self-isolation is more costly. Third, it is best to vaccinate people
who tend to interact often and more than is socially optimal — while being careful not to
incentivize further suboptimal interaction — because they impose large costs on others.
Finally, to get the largest spillovers from vaccinating the most exposed people, policymakers
should discourage increased interaction in response to falling infection rates.
Nikhil Vellodi is an assistant professor at the Paris School of Economics, and Joshua Weiss is
a postdoctoral economist in the Research Department at the Federal Reserve Bank of
Richmond. In the fall, Weiss will be joining the Institute for International Economic Studies

at Stockholm University as an assistant professor.


For a recent paper that studies optimal vaccination taking as given individual behavior and

infection rates, see Ana Babus, Sanmay Das and SangMok Lee, "The Optimal Allocation of Covid19 Vaccines," Covid Economics 44, Centre for Economic Policy Research, Aug. 25, 2020, pp. 47–71.

See World Health Organization Regional O ce for Europe, "Pandemic Fatigue: Reinvigorating
the Public to Prevent COVID-19," revised in November 2020.

For a comprehensive review, see Sebastian Funk, Marcel Salathé and Vincent A. A. Jansen,

"Modelling the In uence of Human Behaviour on the Spread of Infectious Diseases: A Review,"
Journal of the Royal Society Interface, Sept. 6, 2010, vol. 7, no. 50, pp. 1247–1256.

For a recent example focused on the HIV/AIDS epidemic in Malawi, see Jeremy Greenwood,

Philipp Kircher, Cezar Santos and Michèle Tertilt, "An Equilibrium Model of the African HIV/AIDS
Epidemic," Econometrica, July 2019, vol. 87, no. 4, pp. 1081–1113.

Nikhil Vellodi and Joshua Weiss, "Optimal Vaccine Policies: Spillovers and Incentives," Federal
Reserve Bank of Richmond Working Paper No. 21-06, March 2021.

This article may be photocopied or reprinted in its entirety. Please credit the authors,
source, and the Federal Reserve Bank of Richmond and include the italicized statement
Views expressed in this article are those of the authors and not necessarily those of the Federal
Reserve Bank of Richmond or the Federal Reserve System.

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