Results

To illustrate the qualitative nature of optimal dynamic prioritization, we first present results from a single “base” scenario, representing a plausible set of parameters (detailed in SI Appendix, Table S1). These results are then compared to a set of alternative model scenarios as described in Table 1. While we begin with base scenario results, we emphasize the sensitivity analysis under alternative scenarios that follows, since information about some input parameters—for example, expected vaccination supply—continues to change with time. In Fig. 2, the base model allocation decisions are shown for each monthly decision period (in percent of vaccine supply) and then cumulatively (in percent of group vaccinated) at 3 and 6 mo, respectively. Broadly, we find that the optimal policy is very dynamic: Specific groups are targeted each period, and these targets shift over time. Furthermore, targeting is very narrow initially, but then becomes less so as a larger fraction of the population has been covered.

Fig. 2.

The optimal allocation of vaccines (vertical axes) between demographic groups for each decision period (horizontal axis) under the base scenario (A). The rows represent each objective, to minimize deaths (Top), minimize YLL (Middle), and minimize infections (Bottom). The bars for the six decision periods show the percentage of vaccines allocated to a specific group (indicated by a letter, color, and asterisks indicating essential worker groups) in that period. B shows cumulative measures at the end of months 3 and 6, respectively, for the percent of each group that has been vaccinated. The whiskers on each bar represent the sensitivity of the optimal solution to small deviations in the outcome, specifically, the range of allocations resulting in outcomes within 0.5% of the optimal solution.

Table 1.

Descriptions of alternative scenarios relative to the base model (see SI Appendix, section A for specific levels)

Scenario	Change from base scenario parameters	Source
Base scenario	None (Base parameter values are provided
	in SI Appendix, section A)
High initial infections	Increased number of initial symptomatic	Assumed: pandemic state will
	infections (300% increase)	vary between localities when
		vaccine first available to the
		general public
Strong NPI	NSD NPI are strong, resulting in	Consistent with $$ R<1$$
	a declining infection rate
Weak NPI	NSD NPI are weak, resulting in a sharply	Consistent with $$ R\gg 1$$
	increasing burden of infection
Weak vaccine	Lower vaccine effectiveness (success rate) for	Minimum value required by
	all age groups relative to the base scenario	FDA guidelines
Weak vaccine 60+	Lower vaccine effectiveness for	Informed by influenza vaccine
	ages $$ 60+$$ y	effectiveness
Even susceptibility	All ages are equally susceptible to infection;	Assumed: tests sensitivity
	increase in susceptibility for ages $$ <20$$y	to age-dependent susceptibility
	relative to Base	described by refs. 9 and 20
Low supply	Sufficient supply for 5% of the population	Assumed: vaccine supply is
	monthly (50% of supply relative to base	uncertain and known to impact
	scenario; prioritization changes every 10% of the	optimal allocations (21)
	population vaccinated, such that decision
	period is 2 mo)
Ramp up	Vaccine supply is 5% per month for	Informed by comments from
	the first 2 mo and 10% per month thereafter	the scientific head of the US
	(first decision period is 2 mo, so increments	vaccine development
	of 10% of the population are vaccinated each	program (22)
	decision period)
Open schools	Rate of social contact in schools increased	Assumed: tests sensitivity of
	from 30% in base model to 70%	optimal allocations to school
		closure intensity
High contacts	Increased number of contacts outside	Assumed: tests sensitivity to
	the home, school and workplace (50% increase	relaxed distancing
	relative to base)

The whiskers on bars in Fig. 2 show the range of alternative allocations that still produce an outcome that is within 0.5% of the optimum. These indicate that the optimized outcome is relatively sensitive to substitutions between groups for the first 3 mo, as indicated by narrow whiskers around the cumulative allocations. There is, however, some limited ability to substitute vaccines between the two essential worker groups in the first 2 mo when minimizing YLL or deaths. As the size of the susceptible population declines due to vaccination and infections, the optimized outcomes become less sensitive to substitutions (longer whiskers), with shifts between nearly all groups possible without substantial sacrifice. This suggests that targeting strategies can become less strict over time as the most vulnerable populations are protected. Comparing individual periods (Fig. 2A) and cumulative measures (Fig. 2B) shows that whiskers represent a combination of substitution between groups as well as between periods for the same group.

Across objectives, there are substantial differences in which groups are targeted early on. When minimizing deaths, targeting progresses from essential workers (20 y to 39 y*, 40 y to 59 y*), to the oldest (75+ y), and then younger seniors (60 y to 74 y) (Fig. 2). These groups are a mix of those at high risk of mortality (older groups) and high risk of contraction and spread (essential workers). When minimizing YLL, younger seniors are targeted earlier (given their longer average years of life remaining).^‡ Finally, when minimizing infections, we find that younger essential workers take top priority, followed by older essential workers and school-age children (5 y to 19 y), since these groups have higher contacts and thus higher risk of contraction and spread.

In Fig. 3A, we show the dynamic path of infections, starting from the period in which vaccines become available, under various policies. As expected, infections are highest given no vaccines. Results for allocating vaccines in a manner proportional to each group’s size shows the substantial value of even “untargeted” vaccines. As expected, the policy for minimizing infections leads to the lowest level of infections.

Fig. 3.

The number of infections per 1,000 individuals over time under reference policies (no vaccines; untargeted vaccine allocation) and optimized policies minimizing (min) a given metric (A) and the performance of each optimized policy relative to an untargeted allocation policy (B) for the base scenario. The bars are boxed by each resulting metric, colored by the objective driving each policy, and textured to reflect any constraint considered (e.g., age-only or static policies).

In Fig. 3B, we show the performance of various policies for resulting outcome metrics (infections, YLL, and deaths) in terms of the percentage improvement relative to an untargeted vaccine allocation. We consider the optimal policies presented in Fig. 2 where the objective is minimizing infections (green), YLL (purple), or deaths (orange) with no constraints (“none”). We also consider two constrained alternatives: an “age-only” dynamic policy that does not differentiate by essential worker status, and a “static” policy where the fractional allocation across groups does not change over decision periods.^§ We find that the unconstrained policy—that is dynamic and differentiated by essential workers—outperforms the untargeted approach by approximately 31 to 40% depending on the objective. Relative to the unconstrained policy, the age-only and static policies perform substantially worse for infections and YLL, although not for deaths. However, even while the age-only and static policies do not substantially impede performance in minimizing deaths, these constrained approaches still suffer substantial performance loss (9 to 18 percentage points) in the other two outcomes not optimized (YLL and infections) but clearly still of interest.^¶ In other words, accounting for both essential workers and a dynamic prioritization strategy provides substantial improvements in the metric being optimized and/or the other two metrics of interest.

In general, we find that, no matter the policy objective pursued in targeted vaccine allocation, some improvement is made on all three metrics. However, there are trade-offs in what can be achieved between the objectives. For example, policies that minimize infections result in substantially more deaths than a policy that minimizes deaths. We also find that differentiating essential workers substantially reduces these trade-offs between objectives relative to age-only or static policies.

Sensitivity of Vaccine Prioritization.

To assess how robust our base scenario findings are to key uncertainties in the model, we conduct three different sensitivity analyses. First, we consider a set of 10 alternative plausible scenarios involving a broad set of model inputs; then, we focus on a narrower set of four parameters, each explored in richer gradient detail; finally, we examine a few fundamental changes to model structures.

A broad set of alternative scenarios.

We solved for the optimal vaccine allocation across a range of 10 alternative scenarios selected to assess sensitivity to key assumptions of the base model. Differences between these scenarios and the base case are detailed in SI Appendix, Table S1. Relative to the base model, in these alternative scenarios, we consider higher initial infections, stronger or weaker nonsocial distancing (NSD) nonpharmaceutical interventions (NPI) like mask wearing, weaker vaccine effectiveness overall or for seniors (60+ y), lower vaccine supply or supply that starts low and ramps up, more open schools, or higher contact rates overall.

To compare and contrast optimal early vaccination allocation for each scenario and objective, in Fig. 4A, we show the percentage of each group vaccinated after 30% of the overall population is covered (typically in 3 mo, except for alternative supply scenarios). We find that high priority groups—by percent of group vaccinated—are typically but not always robust to the alternative scenarios. For example, when deaths are considered (Fig. 4 A, Top), we see substitution between younger essential workers (29 y to 39 y*) and ages 60 y to 74 y, and, when YLL are considered, there is substitution between younger essential workers and ages 75+ y. To illustrate differences in the relative order of these high-priority groups, in SI Appendix, Fig. S5, we show optimal prioritization of vaccination in the very first decision period across objectives and scenarios. We find that, when YLL are considered, essential workers ages 40 y to 59 y are the highest-priority group in all scenarios. However, when deaths are considered, ages $$ 75+$$ y are the highest-priority group under several alternative scenarios.

Fig. 4.

The cumulative percent of each demographic group (horizontal axis) vaccinated after the first 30% of the population is vaccinated under the alternative scenarios (vertical axis) and each objective to be minimized including deaths (Top), YLL (Middle), and infections (Bottom) (A); init. infect., initial infections. The percentage of additional YLL in excess of the optimum when applying a policy for a given alternative scenario (row) when a particular scenario is the “truth” (column) (B). *, indicating essential worker groups.

For insight into the cost of error in specifying the correct scenario, we assessed the performance of the policy identified for each of the 11 alternative scenarios, depending on which of these 11 is the “true” scenario. In Fig. 4B, we show these results for the YLL objective. For example, the first column shows the performance loss (in percentage of additional YLL above the optimum) when the true scenario is the base model but the decision maker applies a policy matched to any of the alternative scenarios (rows). By construction, when the policy applied matches the true scenario, the performance loss is zero. When YLL is the focus and the base specification is the “true” scenario, the greatest performance loss (9%) comes from mistakenly applying the high initial infections policy.

We find that performance costs, in percentage terms, from applying the wrong policy from this set are typically modest (low single digits), albeit with notable exceptions. For example, when the “truth” is that we have a weak vaccine for ages 60+ y, several policies applied perform very poorly relative to the true optimal policy, since they substitute vaccine away from younger essential workers to ages 75+ y. A few of the policies were generally less robust across various true models, specifically, those for high initial infections, strong NPI, and weak vaccine 60+. The base scenario policy performed reasonably well across true alternative models, with the largest loss arising (7%) when children are not less susceptible (even susceptibility).

Equivalent versions of Fig. 4B for minimizing deaths or infections are provided in SI Appendix, section C. When the focus is minimizing deaths, the pattern of performance between scenarios is very consistent with YLL in Fig. 4. However, the scope for performance loss is larger overall—up from a maximum of 26% for YLL to 46% for deaths. When the focus is infections, the range of performance loss is much less intense, at 7%. For infections, this relatively robust performance arises because optimal policies are much more similar across scenarios when minimizing infections (compared to the other objectives). Given greater scenario-driven heterogeneity in policies for minimizing YLL or deaths, there is greater opportunity for performance loss from specification error.

A gradient over four key parameters.

For further sensitivity analysis, as shown in Fig. 5, we assessed how optimal vaccine allocation policy changed along a gradient for four key model inputs: NSD NPI effectiveness (e.g., mask wearing) which determines the initial reproductive number (when the vaccine first becomes available), initial infections, monthly rate of vaccine supply, and vaccine effectiveness.

Fig. 5.

The total percent of each demographic group vaccinated after 3 mo under the optimal dynamic policy. Each panel shows the effect of varying a key parameter relative to the base model: (A) effectiveness of NPI, which determines the initial reproductive number (when the vaccine first becomes available); (B) monthly rate of vaccine supply; (C) initial infections; and (D) vaccine effectiveness. Base scenario parameter values are indicated with an apostrophe ($$ ‘$$). *, indicating essential worker groups.

Echoing sensitivity results reported above, variation in these parameters had little effect on the optimal policy for minimizing infections. But we found systematic differences in the policies for minimizing YLL and deaths. Essential workers, ages 60 y to 74 y and ages 75+ y, remained the highest-priority groups across the full range of parameters tested, but there was substitution between younger essential workers (29 y to 39 y*) and the older age groups.

In most instances, the percent of vaccines responded in relatively monotonic fashion as parameters varied. For example, consider the objective of minimizing deaths. As depicted in Fig. 5, prioritization of essential workers fell and 60+ y or 75+ y increased as 1) initial infections grow, 2) vaccine supply decreases, or 3) vaccine effectiveness increases. In a few instances, the percent of vaccine allocated to a given group responded nonmonotonically to variation in the parameter. For example, for effectiveness of NPI in Fig. 5A, the allocation skewed toward 75+ y and away from essential workers when the parameter was very high and very low.

These results indicate that, when focusing on deaths or YLL, if transmission cannot be reduced quickly by the vaccine—due to limited supply, high reproductive numbers, or large initial number of infections—typically, this initial supply is most efficiently used to directly protect individuals with the greatest risk of death if infected. This pattern differs for vaccine effectiveness: We find that, as the effectiveness of the vaccine decreased, supply is substituted away from the older (higher risk) age groups to essential workers. This difference is consistent with the fact that, as vaccines become less effective for a given individual, protecting vulnerable individuals is better achieved by reducing population-level transmission.

Changes to model structures.

As a final sensitivity analysis, we examined robustness of the results to three alternative model structures: 1) clustered essential workers, where essential workers only contact other essential workers in the workplace; 2) concentrated essential workers, where, relative to the baseline scenario, the portion of the working age population deemed “essential” is half (20%), and they have approximately double the contact rate; and 3) leaky vaccine, where, rather than working perfectly for 90% of individuals, vaccinated individuals have reduced susceptibility to infection, infectiousness, and risk of death if infected. A more detailed discussion of these models is included in SI Appendix, section D.

We found that the qualitative nature of the solutions remained constant across each of these alternative models, with some minor differences. Treating the essential worker group as a cluster increased the proportion of vaccine allocated to ages 60+ y when deaths and YLL were considered. This shows that, when essential worker contacts are clustered within group, this reduces the indirect protection that vaccinating these individuals provided to others. Conversely, concentrating the essential worker group (to a more select group with higher contact rates) increased the fraction of these individuals vaccinated. This shows that select essential workers with especially high contact rates (e.g., medical professionals and essential retail workers) are particularly strong candidates for early vaccination.

Discussion

Key insights and results from our analysis are summarized in Box 1. Together, these lessons show the strong implications of considering dynamic solutions, social distancing, and essential workers (given their limitations in social distancing) for vaccine prioritization.

Our analysis of COVID-19 vaccine prioritization uniquely accounts for two critical needs: 1) dynamic prioritization given gradual rollout of vaccine during an active pandemic, and 2) attending to substantial heterogeneities in work contacts among the adult population due to the ability of many to work from home. These two novel features demonstrably change optimal vaccine prioritization. Given gradual vaccine deployment, static policies are out-performed by dynamic policies, which narrowly target a small number of demographic groups and (after substantial coverage of them) switch to lower-priority groups. Static policies identify a set of high-priority groups but not how to order them when phased deployment is necessary. More strikingly, targeting essential workers (or other adults with a large number of work contacts) reduces not just the adverse outcome of focus but also trade-offs for remaining outcomes. For example, when minimizing deaths, allocation that differentiates essential workers substantially lessens the degree to which infections and YLL climb from the minimum achieved when each is optimized on its own.

Existing published analysis of optimal COVID-19 vaccination targeting includes Matrajt et al. (16) and Bubar et al. (17). Before comparing and contrasting results, some key modeling differences should be noted. These two analyses consider a wider range of vaccine availability than considered here. Our analysis uniquely incorporates NPI, including social distancing and NSD (e.g., mask wearing). Doing so allows us to account for differences between groups like essential workers constrained in distancing versus others who are much less so. All three preprints implement static optimization where vaccines are allocated and administered in a one-shot process. Our allocation is dynamic, responding to changing epidemiological conditions over a 6-mo period. Finally, all three model vaccines as “leaky,” that is, reducing the probability that a susceptible individual will be infected [and the probability of severe disease (19)]. Bubar et al. also consider an “all-or-nothing” vaccine that is 100% effective for a fraction of the population. In our base model, the vaccine is “all-or-nothing,” although we also consider a leaky vaccine, as discussed at the end of Results.

Matrajt et al. (16) found that optimal strategies to minimize deaths and YLL will either exclusively target groups with high infection fatality rates, maximizing the direct benefit of vaccines, or will target groups with high rates of infection, maximizing the indirect benefits of the vaccine. In contrast, our results indicate that optimal policies initially target groups with high risk of infection and then switch to targeting groups with high infection fatality. This difference most likely follows from our dynamic versus static allocation. The switching behavior we identify is consistent with past work on pandemic influenza vaccine prioritization, which suggests that, early in an outbreak when the infection rate is growing, targeting spread (maximizing indirect benefits) is more efficient, but, later, when the infection rate is leveling off or declining, maximizing direct protection is most efficient (21).

Bubar et al. (17) found that prioritizing adults older than 60 y of age is a robust strategy for minimizing deaths. In contrast, we find that working-age adults are a key priority group, particularly older essential workers. These differences may arise from either our allowance for social distancing and/or dynamic allocation. Our accounting for social distancing on COVID-19 transmission increases the modeled benefits of targeting essential workers, who are less able to substantially reduce their social contacts than individuals over 60 y old. Furthermore, as discussed above, the ability of dynamic policies to switch over time allows the allocation schemes we discuss to capture the benefits of using the initial vaccine supply to slow transmission without sacrificing direct protection of more-vulnerable individuals later on.

Two notable additional analyses of optimal COVID-19 vaccination targeting in preprint form include Wang et al. (23), who focus on the mortality costs of delay in vaccine rollout and the trade-off between prioritizing first versus second doses, as well as Hogan et al. (19), who examine ideal allocation both within and between countries.

National and international institutions have also begun to disseminate guidance. In particular, general guidelines for vaccine prioritization have been put forward by Strategic Advisory Group of Experts of the WHO (24) and the US CDC’s ACIP (25). For example, CDC recommendations prioritize: 1) health care personnel; 2) residents of long-term care facilities; 3) persons aged 75 y and over and frontline essential workers; 4) persons aged 65 y to 74 y, persons aged 16 y to 64 y with high-risk medical conditions, and essential workers; and 5) everyone aged 16 y and over remaining. Categories A and B are subgroups at a finer scale than considered here, although with clear logic supporting top priority. Notably, a clear priority is not set between persons aged 75 y and over and frontline essential workers. This is consistent with our findings, in that prioritization within this pair was sensitive to specific conditions, which will vary over location. Our recommendations differ in the distinction made here between younger and older essential workers, with priority on the latter motivated by increasing mortality from infection with age. The CDC guidelines also consider underlying health conditions, a salient distinction not considered here. WHO guidelines—written more broadly for a global audience—agree on the prioritization of frontline health care workers at high risk of infection, followed by older adults. However, subsequent priority focuses on various sociodemographic groups at high risk (e.g., those in poverty) and essential educational workers before turning to essential workers more broadly.

Although our model provides useful insight for the policy-making process, a number of caveats are in order. In reality, the risk of infection varies continuously across individuals, even between different “essential” occupations. While our model is unique in capturing differences between essential and nonessential workers, the representation of these differences is simplified by averaging the total number of contacts over a group with high work contacts (essential workers) and a group with lower rates of work contacts. This allows us to demonstrate the importance of this heterogeneity in the adult population relative to the standard age-only models, indicating that policy makers should strongly consider occupation-differentiated vaccine allocation strategies.

While we explored a large set of alternative scenarios, further extensions remain for future work. For example, if certain groups (e.g., children or seniors) experience significant vaccination side effects, prioritization might shift away from these groups (26). From a logistical perspective, vaccination will occur through various points of contact with the community (pharmacies, clinics, schools, etc.). Constraints imposed by the distribution network used will affect the relative costs of reaching various subgroups. While the longevity of immunity to COVID-19—either following natural infection or vaccination—is not yet well understood, emerging analysis suggests that, following infection, “durable immunity against secondary COVID-19 disease is a possibility for most individuals” in the sense that immune memory was present in approximately 95% of individuals studied 5 mo to 8 mo after symptom onset (27). How long lasting immune memory will be in the longer run is a key unknown. We assume immunity spans at least through the end of our 6-mo time horizon. However, if, instead, this durability is more limited and/or already waning for those infected early in 2020, we might expect the symptomatic infections curve (Fig. 3A) to stretch farther out and for ideal vaccination strategies to shift toward direct protection of older, vulnerable populations.

From a behavioral perspective, vaccine hesitancy may influence the ability to achieve vaccination priorities, especially as coverage of the population increases. In general, we find that it is not necessary or even ideal to vaccinate all of the susceptible individuals in a demographic group, at least given the level of 60% of the population vaccinated considered here. Thus, at least initially, some level of vaccine hesitancy may have limited material impact. However, hesitancy may play a more significant role in the longer run, especially if hesitancy rates are large and herd immunity proves difficult to achieve (e.g., if vaccine effectiveness is low, and/or NPI relaxation is aggressive). Vaccine hesitancy that is concentrated in a particular community or demographic group could also change the optimal prioritization strategy. Similarly, adjustments would be needed if groups differ in the duration of vaccine effectiveness or diligence in obtaining a second dose of the vaccine where (and when) necessary.

For simplicity, we limited policy objectives to a set of concise metrics of health outcomes (minimizing expected cases, YLL, or deaths). However, other health-related metrics such as protecting the most vulnerable and social values such as returning to school, work, and social life are important to consider. Our analysis reveals that optimal strategies for minimizing deaths and YLL are broadly aligned with the goal of protecting the most vulnerable. These solutions target essential workers who are the least able to participate in NPI such as social distancing and thus are the most at risk for infection, and individuals over the age of 60 y who have the highest risk of death if infected by the disease. Other social values such as returning to school will most likely change the allocation schemes to offset the risk created by relaxing social distancing. For example, if allowing children to return to school was a high priority, then allocation strategies might be tilted toward targeting school-age children and teachers. A detailed analysis of optimal vaccine allocation given the relaxation of social distancing to achieve particular social objectives is a key direction for future research.

Methods

Social Distancing.

Expression of symptoms and social distancing policies are likely to change individuals’ behaviors over time. To model these changes, we scaled the contribution of each contact matrix for location $$ x$$,

$r_m=\sum _x{\alpha }_{m,x}{r}_x.$ [1]

The weights $$ {\alpha }_{m,x}$$ depend on disease and symptom status ($$ m$$) and location ($$ x$$) as specified in Table 2. We scaled social contacts for symptomatic individuals following changes in behavior observed among symptomatic individuals during the 2009 A/H1N1 pandemic (30). For those without symptoms (susceptible and asymptomatic), the weights were specified to match reduced levels of social contacts as the product of social distancing policies. Home contact rates were held constant, and nonhousehold contact rates were roughly based on survey data from ref. 15. However, levels of social distancing have varied strongly over time and between locations. To account for this variability, we tested a range of alternative levels in addition to the base model. The results for these alternative parameter values are discussed in SI Appendix, section A. Also, notably, we do not consider the seasonality of contact rates for children in the scenarios where schools are modeled as closed. This would likely have limited impact on the optimal solutions, but, when this is not the case, we may overestimate or underestimate the importance of school contacts, depending on the time of year when vaccines are distributed.

Table 2.

Weights on contact rates for a given disease and symptom type ($$ m$$) and location/activity ($$ x$$) under social distancing

	Contact rate weights, $$ {\alpha }_{m,x}$$
Disease and symptom type	Home	Work	School	Other
Symptomatic	1.0	0.036	0.036	0.075
Susceptible or asymptomatic	1.0	0.4*, 0.1	0.3	0.4

When essential and nonessential worker weights are both needed, the former is marked with an asterisk.

The proportion of essential workers in the population was set to be consistent with estimates of the portion of jobs that can be done from home (31) and estimates from the US Cyber-security and Infrastructure Security Agency, which indicate that 70% of the workforce is involved in these essential activities (e.g., healthcare, telecommunications, information technology systems, defense, food and agriculture, transportation and logistics, energy, water, public works, and public safety) (32). However, essential workers are not a cleanly defined group of individuals, and there is heterogeneity in the level of contact rates within this group. As a robustness check on this base scenario approach, we also tested a model with a smaller number of essential workers with higher contact rates. Results from this model are discussed in SI Appendix, section D.