Evaluating primary and booster vaccination prioritization strategies for COVID-19 by age and high-contact employment status using data from contact surveys

The debate around vaccine prioritization for COVID-19 has revolved around balancing the benefits from: (1) the direct protection conferred by the vaccine amongst those at highest risk of severe disease outcomes, and (2) the indirect protection through vaccinating those that are at highest risk of being infected and of transmitting the virus. While adults aged 65+ are at highest risk for severe disease and death from COVID-19, essential service and other in-person workers with greater rates of contact may be at higher risk of acquiring and transmitting SARS-CoV-2. Unfortunately, there have been relatively little data available to understand heterogeneity in contact rates and risk across these demographic groups. Here, we retrospectively analyze and evaluate vaccination prioritization strategies by age and worker status. We use a mathematical model of SARS-CoV-2 transmission and uniquely detailed contact data collected as part of the Berkeley Interpersonal Contact Survey to evaluate five vaccination prioritization strategies: (1) prioritizing only adults over age 65, (2) prioritizing only high-contact workers, (3) splitting prioritization between adults 65+ and high-contact workers, (4) tiered prioritization of adults over age 65 followed by high-contact workers, and (5) tiered prioritization of high-contact workers followed by adults 65+. We find that for the primary two-dose vaccination schedule, assuming 70% uptake, a tiered roll-out that first prioritizes adults 65+ averts the most deaths (31% fewer deaths compared to a no-vaccination scenario) while a tiered roll-out that prioritizes high contact workers averts the most number of clinical infections (14% fewer clinical infections compared to a no-vaccination scenario). We also consider prioritization strategies for booster doses during a subsequent outbreak of a hypothetical new SARS-CoV-2 variant. We find that a tiered roll-out that prioritizes adults 65+ for booster doses consistently averts the most deaths, and it may also avert the most number of clinical cases depending on the epidemiology of the SARS-CoV-2 variant and the vaccine efficacy.


Introduction
COVID-19 vaccines have been shown to be highly effective at preventing severe illness and death (Baden et al., 2021;Polack et al., 2020). Following the introduction of vaccination in the U.S. in December 2020, infection rates decreased dramatically through the first quarter of 2021 as increasing shares of the population were protected via vaccine-derived immunity (Gupta et al., 2021). Due to a limited vaccine supply initially, there has been a complicated debate around the trade offs of vaccine prioritization strategies for adults over age 65, healthcare workers, other essential frontline workers, and the general public (Schaffer DeRoo et al., 2020;Persad et al., 2020Persad et al., , 2021Giubilini et al., 2021).
Control interventions for infectious diseases can have different public health objectives: while the highest priority is often to limit total at reducing total hospitalizations and deaths due to COVID-19. On the other hand, in-person workers with higher rates of person-to-person contacts are at an increased risk of being infected with and transmitting SARS-CoV-2.
Thus, vaccine prioritization strategies need to balance: (1) the direct protection conferred by the vaccine amongst those at highest risk of severe disease outcomes, and (2) the benefits of indirect protection and potentially achieving herd immunity more quickly through vaccinating those that are at highest risk of being infected and of transmitting the virus. The indirect benefits of preventing COVID-19 by prioritizing high-contact workers could outweigh the direct benefit of vaccinating adults 65+, depending on the public health objective, the prevalence of non-pharmaceutical interventions, and the epidemiology of the virus (Buckner et al., 2021).
Vaccinating high-contact workers also has important implications for social and economic equity. Historically-disadvantaged groups, especially Blacks and Hispanics, are over-represented in essential and front-line occupations and have younger age-distributions compared to Whites (Nelson et al., 2022). Prioritizing high-contact workers, therefore, delivers proportionally more doses to racial and ethnic groups that have also been hardest hit by the pandemic (Andrasfay and Goldman, 2021;Wrigley-Field et al., 2020 compared to a purely age-based prioritization. In the US, distribution of the primary vaccine doses prioritized a combination of adults 65+ and essential workers in progressive phases, beginning with those living in long-term care settings and healthcare workers. Eligibility was first opened to adults 65+ and to certain occupational groups before opening to the general public (Dooling, 2021). The debate on prioritization is, however, still relevant in many other parts of the world, as well as in the US for future booster doses. It is also important to retrospectively evaluate prioritization strategies to inform response to future pandemics. Mathematical models that account for both the direct and indirect effects of vaccination can help guide policy decisions on prioritization. However, there are little data on contact rates by worker status and age available for the U.S., making these models hard to parameterize. The relatively few contact surveys conducted during 2020-2021 indicated that total contacts had substantially reduced compared to pre-pandemic measures Feehan and Mahmud, 2021). However, previously available data have reported contact rates disaggregated by age, but not by both age and occupational status. In a survey of workers in the US, Kiti et al. (2021) found median number of reported contacts was low (around two) and that household structure -rather than age or race -was responsible for the variation in contacts between respondents. However, the study was limited to only three US companies, where many workers reported being able to work remotely offsite. A nationally representative study, covering a more diverse range of occupations, reported that most contacts during this period did happen at work, and that nonwhite and workers in essential occupations had amongst the highest total contact rates (Nelson et al., 2022). Here, we retrospectively analyze and evaluate vaccination prioritization strategies by age and worker status using detailed contact data from surveys to parameterize a mathematical transmission model for SARS-CoV-2.
We compare total effects of prioritizing adults 65+ for vaccination versus prioritizing workers who potentially have a higher risk of contracting COVID-19 due to their in-person work status (Baker et al., 2020;Hawkins, 2020;Selden and Berdahl, 2020). The model accounts for contact patterns between age and occupation groups using contact survey data collected as part of the Berkeley Interpersonal Contact Survey (BICS; Feehan and Mahmud, 2021), which has been collecting detailed information about a respondent's daily behavior and their disease-relevant interpersonal contact since March 2020.
We find that prioritizing adults 65+ for primary vaccination averts 25% more deaths than prioritizing high contact workers and 11% more than a split strategy. However, the most clinical infections are averted by strategies that prioritize high contact workers first. We extend the model to consider the prioritization of booster doses during a hypothetical future outbreak of a new SARS-CoV-2 variant that is able to partially evade vaccine-derived immunity from primary vaccination. When considering booster doses, the reduction in deaths is greatest when prioritizing adults 65+, but all three strategies have similar effects on clinical infections. These results highlight the impact of various vaccination prioritization strategies and can help guide policies during future outbreaks.

Data
The BICS survey, collected in several waves beginning in March 2020, is an online survey aimed at capturing the frequency and nature of respondents' physical and conversational contacts over a 24-h period. Respondents (egos) in the BICS survey are asked about members of their household and their total number of non-household contacts, as well as detailed information on up to 3 of their previous day's contacts (alters). Here we use data from wave 4 of the BICS survey, collected between November 30th and December 8th, 2020, where 2993 respondents provided detailed information on 10,001 contacts and were asked additional questions on their work status and work contacts. Respondents who reported being employed were asked to indicate the number of close contacts they had while performing duties for their job.
Respondents are divided into 3 categories: low contact (LC) adults (age 18-64) not reporting having any close work contacts, high contact (HC) adults (age 18-64) reporting having work contacts, and adults 65+. Although heterogeneity in contact rates and mortality may exist within groups, these age groups were chosen to maintain sufficient sample size especially in the oldest age group. 34% of respondents aged 18-64 reported having interpersonal contacts at work and are labeled as high contact (HC). Children (under age 18) were not included in the survey, although adult respondents could report their contact with children. The procedure for estimating contacts for the 0-18 age group is described below. Alters are divided into children aged 0-18, adults 18-64, and adults 65+ and weighted by the number of total close contacts reported by each ego (see Feehan and Mahmud (2021) for more detail on the weighting procedure). Working-age alters aged 18-64 are categorized as being work contacts if the reported relationship was a coworker or client or if the reported contact happened at work or a store. This consisted of 22% of reported contacts for adults aged 18-64. For some working-age alters we were unable to determine work status from the survey data. This was due to missing data for nonhousehold alters on the purpose of the reported contact and for all reported household contacts (since their work status was not collected). For the alters whose in-person work status is indeterminable from the survey data provided, alters are randomly re-labeled as having inperson work such that the proportion of high contact alters matched the surveyed ego proportion. We also perform a sensitivity test to understand the impact of this random reallocation.
The survey responses are used to construct an age and work-status structured contact matrix between children, low-contact adults (18-64), high-contact adults (18-64), and adults 65+ ( Fig. 1 and supplementary S1.1-S1.2) using standard methods described in more detail by Feehan and Mahmud (2021) and Jarvis et al. (2020). Briefly, the raw contact matrix has entries corresponding to the average number of daily contacts between respondents (ego) in group with their reported contacts in group , adjusted for survey weights. Total contacts in a population must be reciprocal, but may not be in the survey data due to sampling and differences in survey reporting. We impose reciprocity using previously described methods (Feehan and Mahmud, 2021). To adjust for reciprocity, population data for each group is taken from the American Community Survey (ACS) 2019 5-year estimates (US Census Bureau, 2019). Adults aged 18-64 in the ACS are categorized E. Roubenoff et al. as working in-person (34%) and not working in-person (66%) using the survey proportions since equivalent data on in-person work status is unavailable from the ACS. As children are not included in the BICS survey, contacts between children are derived from the POLYMOD survey as described in the supplementary materials section S1.3. The reciprocal contact matrix, , is the reciprocity-enforced average daily contact matrix. We note that respondents in our survey in the 65+ and Adult LC categories have comparable rates of contact to the survey of remote workers conducted by Kiti et al. (2021).

SARS-CoV-2 transmission model
To model SARS-CoV-2 transmission dynamics and COVID-19 incidence and mortality, we use a deterministic, continuous time compartmental model (outlined in the supplementary section S1.4, similar to Bubar et al. (2021) and Buckner et al. (2021)). The model allows for heterogenous mixing between age and in-person employment status groups as specified by the contact matrix derived from the BICS survey data. Susceptibles 1 (compartments and , described below) who are exposed to SARS-CoV-2 enter an exposed (latent) phase ( ). Depending on their age group, exposed individuals proceed to have clinical (symptomatic) infection ( ) with probability [0.35, 0.4, 0.75] for children, adults 18-64, and adults 65+ respectively; remaining cases experience subclinical (asymptomatic) infection ( ; adapted from Davies et al. (2020)). We allow for subclinical transmission, at a reduced probability (50%; Davies et al., 2020) relative to clinical infections. Probability of death after clinical infection ( ) varies according to age; subclinical mortality is assumed to be zero. Fatal cases proceed to compartment and non-fatal cases recover to compartment . We model a two-dose primary vaccination schedule, distributed 25 days apart, to match the two-dose Pfizer and Moderna vaccines that account for the majority of the vaccination doses delivered in the United States (CDC, 2020). Susceptibles awaiting the vaccine in compartment proceed to compartment after the first dose and then to after the second dose; individuals who have contracted SARS-CoV-2 are ineligible for the vaccine. We incorporate 'leaky' vaccine efficacy and vaccine hesitancy using methods similar to Bubar et al. (2021) and assume an 80% reduction in infections after the first dosage and 90% after the second, consistent with efficacy estimates during the initial roll-out of the vaccines. Leaky vaccines are incorporated by proportionally reducing the force of infection by the corresponding vaccine efficacy for all vaccinated individuals after one or two vaccine doses. In our implementation, vaccination reduces the probability of becoming infected, but does not reduce the probability of a vaccinated yet infectious individual of transmitting the disease (Tenforde, 2021;Thompson, 2021). Breakthrough infections occurring among those who have received either the first or second dose proceed to the exposed compartment and then on to the infected compartments (with the same probabilities as unvaccinated exposed individuals). Vaccine hesitancy is incorporated by imposing a 70% uptake of the primary vaccination doses, derived from the National Immunization Survey's May 2021 primary uptake for seniors (National Center for Immunization and Respiratory Diseases (NCIRD), 2022a,b). At the start of the simulation, 70% of susceptibles are in the compartment and awaiting vaccination; the remaining 30% of susceptibles who refuse or are otherwise ineligible for the vaccine are placed in the compartment , and are otherwise identical to individuals in the compartment. At its peak, nearly 5 million Americans were being vaccinated per day (CDC, 2020); however, as initially vaccine rollout was slower, we assume an average 2 million vaccinations per day distributed equally between first and second shots. First doses are distributed until the compartment is depleted, either through vaccination or infection. Over the course of the simulation, vaccine uptake is less than the 70% of the target population as those who have become infected while susceptible and awaiting vaccination are ineligible for vaccination. After distribution of vaccines to the priority group, vaccines (including surplus doses intended for members of the priority group who became infected and subsequently ineligible) are distributed to any remaining adults 65+, adults 18-64, and children proportional to the remaining susceptible population size in each group. Those who have recovered from infection are not eligible for vaccination in our simulations.
The next generation matrix (NGM; Bansal et al., 2007;Diekmann et al., 2010;Bubar et al., 2021) for the model is: where is the recovery rate, is the probability that an exposed individual in group is clinically infectious, is the relative infectiousness of clinical versus sub-clinical cases, is the age-dependent susceptibility to infection after contact with an infectious individual, and is the entry in contact matrix corresponding to the average number of daily contacts a respondent in group has with an individual in group . The dominant eigenvalue of the NGM is the basic reproduction number , and when the population is fully susceptible this is equal to the basic reproduction number, 0 . We scaled the values of to calibrate to a specific value of 0 by optimizing a scaling factor for such that the largest eigenvalue of the NGM matches an assumed 0 value Bubar et al., 2021;McEvoy et al., 2020).
The starting population for the simulations is the United States population on January 1st, 2021, with approximately 73.4 million children, 200.5 million adults 18-64, and 50.8 million adults 65+ (US Census Bureau, 2019). Working-age adults were split into working in person and not working in person (including unemployed) using the survey proportions of 34% and 66%, respectively, as derived from BICS data. On January 1st, there were 20, 166, 028 confirmed cases, 352,390 deaths, and 11, 426, 602 known active cases (Dong et al., 2020). The starting conditions for deaths, subclinical cases, recovered cases, and exposed individuals are detailed in supplementary section S1.

Model parameters
Estimates for , , and are taken from literature Bubar et al., 2021;McEvoy et al., 2020). To account for uncertainty in other model parameters, we performed 1000 simulations with transmission and mortality parameters drawn from their assumed distributions (described below) using latin hypercube sampling. 0 was assumed to be distributed normally with mean 2.5 and standard deviation 0.54 (following Feehan and Mahmud, 2021). Child, adult 18-64, and adult 65+ mortality were drawn from uniform distributions [0.003%, 0.005%], [0.20%, 0.26%], [6.9%, 10.4%], respectively (bounds for uniform distribution are the 95% confidence intervals from Levin et al., 2020 for age groups 0-34, 45-54, and 75-84). Average latent period is assumed to be distributed uniformly between 2 and 4 days and average duration of infectiousness is assumed to be distributed uniformly between 4 and 6 days, such that median draws follow values assumed by the literature (see supplemental table S1.6 for sources on all parameters). Additional parameters are outlined in table S1.6. For all simulations, we estimated the percent reduction in total clinical infections and total deaths from January 1, 2021 until December 31st, 2021 compared to a no-vaccination scenario for five vaccine prioritization strategies: (1) prioritizing only adults over age 65, (2) prioritizing only adults 18-64 with in-person work contacts, (3) splitting priority vaccines evenly between adults 65+ and adults working in person, (4) a 'tiered' strategy that prioritizes adults 65+ before high contact workers, and (5) a 'tiered' strategy that prioritizes high contact workers before adults 65+ (further details are provided in the supplementary material section S1.3). The 'tiered' strategies are intended to replicate the CDC's decision to progressively distribute the vaccine in a series of decreasing priorities. In our simulations, tiered roll-outs differ from the single priority strategies by allowing a second-priority group to have access to the vaccine before general distribution (when doses are distributed proportionally to eligible group size). For example, for the single priority 65+ strategy, after all of those eligible in the oldest age group have been vaccinated, remaining vaccines are distributed to other groups proportional to remaining eligible group size; however, during the tiered 65+ strategy, after eligible adults 65+ have been vaccinated doses are distributed to eligible HC adults before being distributed to other groups. For clarity, we present the simulation results using the median draw for each parameter for discussion of effect sizes ( 0 = 2.5; = [0.00004, 0.0023, 0.08] for children, adults 18-64, and adults 65+ respectively; latent period = 3 days; and infectious period = 5 days), but show the full range of simulation results across the 1000 parameter combinations.

Booster dose model for a subsequent outbreak of a SARS-CoV-2 variant
We also extend the model (outlined in supplementary material section S1.8) to consider a subsequent outbreak caused by a new, more transmissible SARS-CoV-2 variant, such as the Omicron variant, where vaccines may be less effective (Collie et al., 2022;Hogan et al., 2021;UK Health Security Agency, 2021;Thompson, 2022). In this situation, distribution of a third ''booster'' dose is necessary to increase protection against clinical infection, hospitalization, and death. To maintain consistency across results, the starting population size is the same as in the previous simulation (the US population on January 1st 2021). In the booster simulation, we take the January 1st 2022 estimate of 34%, 78%, and 95% of children, adults 18-64, and adults 65+ as having received a primary course of vaccination (2 doses, represented by compartment ; National Center for Immunization and Respiratory Diseases (NCIRD), 2022a,b). Remaining susceptibles are assumed to refuse the vaccine and are placed in compartment . We assume that 70% of individuals in who have received the two-dose primary course of vaccination will receive booster doses; hesitancy or ineligibility for booster doses is incorporated by moving 30% of these individuals in to , indicating that they decline the booster dose. One million booster doses are distributed daily among individuals in until that compartment reaches zero individuals either through infection or vaccination. In this booster model, no individuals will be present in compartment (awaiting first dose) or (awaiting second dose). We consider the same five strategies as before for priority distribution of booster doses. Since the vaccine's effectiveness in reducing transmission is unknown for primary and boosted individuals for new variants, we conduct 1000 simulations with randomly drawn values for vaccine efficacy from an assumed distribution; we also draw 1000 values of 0 from an assumed distribution. The vaccine efficacy is randomly drawn from distributions derived from the CDC's estimates of vaccine efficacy against the Omicron variant (Thompson, 2022). In these simulations, primary (2-dose) vaccine efficacy is drawn from a uniform distribution between 32% and 43%; vaccine efficacy of the booster dose is drawn from a uniform distribution between 79% and 84%. (Thompson, 2022). Breakthrough infections among individuals who have received 2 or 3 doses of the vaccine proceed through the Exposed and Infectious compartments. A meta-analysis of the Omicron variant's 0 estimates shows considerable variation from 5.5 to 24, with a median of 10 (IQR: 7.25, 11.88; Liu and Rocklöv, 2022). To account for a wide range of transmissibility of potential new variants, we draw 0 uniformly between 2 and 12. All other parameters are held at their median values as above. Similar to the primary simulation, we present results from a simulation with the median draw of all parameters.

Prioritization strategies for primary vaccine doses
For a given combination of simulation parameters, we identify the vaccine prioritization strategies that results in the fewest number of deaths due to COVID-19 and the fewest number of clinical infections. In the simulation with median parameter values, tiered 65+ roll out reduces deaths by 31.32% (723,866 deaths averted) compared to a novaccination scenario. This strategy saves 25.13% (532,567) more lives than prioritizing high contact workers, and 11.49% (206,087) more lives than splitting prioritization between workers and adults 65+. We note that this strategy is only marginally more effective at reducing deaths (0.34%) than prioritizing only adults 65+ before general distribution, indicating that any distribution strategy that gives initial priority to older adults will limit the most deaths. For a tiered 65+ roll out, there is also a modest reduction in clinical infections-13% fewer (10.9 million infections averted) compared to no vaccination. However, we find that the most effective strategy for limiting clinical infections is through a tiered roll-out that first prioritizes high contact workers. This when compared to no vaccination for randomly drawn transmission parameters. The median percent reduction in deaths was highest in a tiered strategy that prioritizing seniors and lowest when only prioritizing contact risk workers; clinical infections are reduced the most by a tiered system that prioritizes workers first, although all strategies produce similar results. (B) and (C): For baseline parameters, trajectories of daily cumulative clinical infections (B) and deaths (C) averted relative to a no vaccination scenario, calculated as the cumulative difference between each strategy and null through each date. For each vaccine strategy, we define deaths or clinical infections averted as the difference between deaths or clinical infections in the null scenario versus the vaccination scenario. When prioritizing seniors the reduction in deaths begins nearly immediately, whereas the indirect benefit from prioritizing HC workers begins later and is lower in magnitude. The opposite is observed for clinical infections. strategy reduces infections by 13.9% compared to no vaccination (11.5 million clinical infections averted), although we note that the reduction in clinical infections is similar among all prioritization schemes. Overall, we find that strategies that prioritize high contact workers, even when split with adults 65+, do limit clinical infections but fail to confer the lifesaving benefit of strategies prioritizing adults over age 65. Fig. 2a shows the percent reduction in deaths and clinical infections relative to no vaccination, across a range of values for the mortality and transmission parameters. Our results are consistent across a wide range of parameter combinations. In 100% of simulations, the tiered 65+ rollout was the most effective strategy for limiting deaths due to COVID-19. All prioritization strategies performed remarkably similarly for reducing the most number of clinical infections. In 62.5% of simulations the tiered HC roll-out was the most effective at limiting clinical infections; in the remaining 37.5% of simulations, the most effective strategy appears to be the tiered 65+ roll-out. Through sensitivity analysis, we show below that these differences are driven by variations in 0 . These results indicate a marked departure from no vaccination between mid January and February. Vaccines reach their peak lifesaving power very quickly within the first month and the relative benefit increases through February. This demonstrates that the timing of vaccines is critical: prioritizing seniors limits the most deaths because they are able to develop vaccine-derived immunity before the peak of the outbreak. Further, tiered roll out strategies show an extended benefit over their single-prioritization counterparts through February and March after distribution of vaccines to the first priority group. Trajectories for each demographic group are shown in the model appendix. Interestingly, when deaths are broken down by age and worker status, the tiered 65+ strategy averts the most deaths only in the adults 65+ E. Roubenoff et al. Fig . 3. Results of the sensitivity analysis of 0 (varied linearly between 1 and 5 in 0.1 increments) and the resultant count of total deaths (A) and clinical infections (B). Across all values, a strategy that prioritizes adults 65+ either directly or in a tiered roll out limits the most deaths. At low values of R0 (<2.5) the reduction in clinical infections is greatest in a 'Tiered HC' roll out; however, the most effective strategy with high R0 is through a Tiered 65+ strategy.
group. For all other groups (children 0-18 and adults 18-64), the tiered HC strategy averts the most deaths. However, since deaths are relatively much higher in the adults 65+ group, the tiered 65+ strategy averts the most deaths in the population overall (see supplemental figure S4).
We conduct additional analyses to test the sensitivity of our results to the choice of simulation parameters. For each simulation, we separately vary 0 between 1 and 5, 65+ between 1% and 10%, and the proportion of priority vaccinations split between high contact workers and adults 65+ between 0 and 1. All other parameters are kept the same as the baseline. We see that for all values of 0 , the deaths are lowest by prioritizing adults 65+ for vaccination (Fig. 3). However, the strategy for averting the most clinical infections is sensitive to 0 , and a cross-over in the most effective strategy to limit clinical infections occurs around 0 = 2.6. When 0 is less than 2.6, prioritizing high contact workers results in the fewest clinical infections. With higher values of 0 , prioritizing adults 65+ leads to the fewest clinical infections. With larger values of 0 , the peak of the outbreak happens earlier in simulation time, resulting in more cases before most vaccines are distributed. Since high-contact individuals in a population will be infected earlier in an outbreak (Mossong et al., 2008) and, therefore, removed from the eligible pool of vaccine recipients, the strategies prioritizing high-contact workers are no longer the most effective for reducing clinical infections for high values of 0 . A strategy prioritizing high-contact workers is, therefore, less effective in reducing clinical infections (compared to a low transmission scenario) since susceptibles in that group will be depleted faster and fewer doses will be distributed to them overall. In a higher transmission setting, the most effective strategy for reducing clinical infections becomes the strategy that targets those most at risk of having a clinical infection: in our model, seniors are almost twice as likely to develop clinical symptoms than adults aged 18-64 (69% vs. 36%). Instead, for high values of 0 prioritizing adults 65+ is most effective both for reducing deaths as well as clinical infections. However, these results are likely dependent on the timing of vaccine introduction and the practicalities of reaching a large enough population for vaccination before the peak of the outbreak.
As expected, the reduction in the number of deaths is highly sensitive to (supplemental figure S7); however, the most effective strategy consistently remains prioritizing adults 65+ for vaccination due to the strong age gradient in mortality. Fig. 4 shows the effect on total deaths and clinical infections as the proportion of vaccinations given to adults 65+ is varied under the split vaccination scenario. Deaths are always minimized when giving 100% of priority vaccines to adults 65+, and total infections are minimized when priority is given to high contact workers. However, we do find a minimum number of clinical infections occurring when 55% of vaccinations are given to seniors. This nonlinearity in clinical infections is a result of the fact that the burden of clinical infections by subgroup is jointly determined by the agedependent susceptibility to infection (higher amongst HC workers) and probability of symptomatic illness (highest amongst adults 65+).

Prioritization of booster doses during a subsequent outbreak
In the simulation conducted with the median parameter draws, prioritization has a smaller effect on relative outcomes for booster doses than the primary doses. A tiered 65+ roll out for boosters not only continues to save the most lives, but in a departure from the primary simulation, also reduces clinical infections the most-although like the primary simulation, the reduction in infections is nearly equal between the three strategies. With median parameter values ( 0 : 7; primary vaccine efficacy: 37.5%; booster vaccine efficacy: 81.5%), a tiered 65+ roll-out reduces deaths by 14.23% (393,562) compared to no booster doses. This strategy reduces deaths by 11.5% more than prioritizing only HC workers and 7% more than a tiered HC roll out. Tiered 65+ roll-out reduces infections by 5.8% (6.5 million infections averted); however, all three strategies reduce infections by nearly the same amount (within 1%). We note that in this subsequent outbreak, the population of eligible HC workers awaiting vaccination is considerably smaller than the primary outbreak; while the eligible 65+ population between the two scenarios is similar (33 million adults 65+ are awaiting primary vaccination in the primary outbreak compared to 31 million for booster doses), the population of eligible high contact workers decreases from about 45 million to about 35 million. This is driven by lower uptake rates of primary vaccination among those below age 65 compared to adults 65+. These results are replicated across the 1000 sets of simulated parameters, shown in Fig. 5. Across all 1000 simulations the median percentage reduction in deaths compared to no boosters is greatest during a tiered 65+ roll out. Clinical infections are reduced the most during a tiered 65+ roll out in 49.1% of simulated parameters; in the other 50.9% of simulations, tiered HC roll out was most effective. Similarly to the primary scenario, this variation in the number of clinical infections averted is driven by 0 .
When 0 is low, HC or Tiered HC prioritization can limit the most clinical infections (Fig. 6). For both deaths and clinical infections the difference between all distribution strategies is smaller when 0 is higher (Fig. 6). Fig. 4. The proportion of vaccines split between seniors and HC workers is varied from 0% to 100% and shown with counts of (A) total infections, (B) clinical infections, (C) total vaccinated, and (D) total deaths. Extremes (corresponding to the HC Prior and 65+ Prior strategies) are shown. When priority vaccines are given more to adults 65+, deaths are minimized but total infections are maximized, indicating that while this strategy limits deaths it fails to limit transmission effectively. Additionally, more susceptibles are eligible for vaccination under this strategy. However, the minimum number of clinical infections is minimized when 59% of vaccines are distributed to 65+. This effect is mediated by increased susceptibility to infection and increased probability of symptomatic infection among seniors, and the increased priority group size among HC workers.

Discussion
While previous modeling studies have evaluated COVID-19 vaccine distribution strategies (Matrajt et al., 2021), Foy et al. (2021); see (Saadi et al., 2021 for a review for 43 such studies), very few had considered heterogeneity in contact rates by both age and worker status. We show, using uniquely detailed contact data, that even when we account for high rates of contact among a sub-group, prioritizing vaccination of the oldest age group averts the most deaths from COVID-19. However, we also find that prioritizing high-transmission groups can limit the spread of disease.
We find that the most effective strategy, given our model parameters, for reducing deaths due to COVID-19 via vaccination was a tiered roll out that first prioritized adults over age 65 followed by high contact workers, with remaining doses split among low contact adults 18-64 and children (Tiered 65+ strategy). However, the most clinical infections are averted through a tiered roll out that prioritized high contact workers followed by adults over age 65 before general distribution (Tiered HC strategy).
The most effective strategy for distribution of booster doses in our model to limit deaths is similar to the primary scenario -it is most effective to prioritize seniors for reducing mortality -and this strategy may also reduce the number of clinical infections the most depending on the transmissibility of the novel variant strain. Without an inflow of susceptibles from births or waning immunity in our model, this difference for booster dose prioritization strategies is driven almost entirely by the lower uptake rate for primary and booster doses by 18-64 year olds compare to adults 65+. However, we note that all three distribution strategies for booster doses result in nearly equal reductions in clinical infections.
These simulations were designed to test the total effect of vaccination -both the direct benefits of vaccination on the prioritized group and the indirect effects of reducing community spread through social contact patterns -using empirical estimates of contact rates across groups. When distributing initial doses, the indirect effects of vaccinating high-risk workers or splitting vaccines between workers and seniors did not confer a greater reduction in deaths than the direct effects of prioritizing all seniors but did reduce the spread of COVID-19 overall.
While limiting deaths is often the primary public health objective, other priorities can include limiting total infections or reducing the number of infected persons at a given time. A healthcare system that is stressed beyond the critical care capacity of ER/ICU admissions may see both increased COVID-19 case fatality and excess secondary deaths (Phua et al., 2020;Miura et al., 2021, andWood et al., 2020). Prioritizing high contact workers with in-person employment may alleviate strain on the healthcare system and reduce the number of people living with chronic COVID-19 symptoms. In a real-world setting, there is undoubtedly a benefit to prioritizing some essential workers in healthcare or eldercare settings who have more exposure to highmortality populations; substantial heterogeneity exists even within our surveyed high risk workers. Results of our 'split' analysis show that when some vaccines for adults 65+ are diverted to high risk workers, fewer deaths are averted, but the total number of clinical infections drops sharply. The most lives are saved when adults 65+ are prioritized, which is consistent with early CDC guidance that prioritized the elderly and a limited number of healthcare workers first.
Public health objectives and the most effective strategy may also depend on the timing of vaccine distribution . For example, Mylius et al. (2008) find that for pandemic influenza, prioritizing the oldest age group is most effective at limiting deaths, but only if distribution begins near the peak of the outbreak; otherwise, prioritizing young adults and schoolchildren for early doses is most effective. Substantial differences in the age-specific contact, mortality, and vaccine uptake indicate that the most beneficial early-target groups for vaccination are considerably different between COVID-19 and influenza (Fitzpatrick and Galvani, 2021). Understanding how the effectiveness of strategies may change over the course of the COVID-19 pandemic is a key direction of future research.
Our results also highlight the significant impact of imperfect vaccines and imperfect vaccine uptake on clinical infections and deaths. We show that the potential disease-averting power of vaccines is lost due to delays in vaccine availability for the general population, as many susceptibles awaiting the vaccine are infected before they are able to be vaccinated (supplementary figure S8). High-contact groups are more likely to be infected earlier in the outbreak, thereby reducing the size of the population eligible for vaccination. This, in combination with low vaccine uptake, reduces the effectiveness of vaccination strategies in high transmission scenarios. This is especially true for the high contact group, who are more likely to be infected earlier on in the outbreak before vaccination is fully rolled out.
Our study has several limitations. First, although our population is faceted by age and employment, the model does not consider other non-pharmaceutical interventions, such as the use of face masks, that can reduce transmission during interpersonal contact. Brief contact between high-risk workers and customers that are masked and distanced may be ultimately insignificant compared to adults lacking such contacts but who are engaging in risky behavior during personal time. Quantifying overall risk along other dimensions of contact, such as whether the contact took place indoors out outdoors, the duration of contact, whether a mask was worn, etc., is an important direction for future research. Second, we are limited -by the survey sample sizeto using only course age and contact status categories in our contact matrix. By including all respondents and their contacts over age 65 in our oldest age group and using the average infection fatality ratio, our analysis may mask important heterogeneity by age in mortality (Levin et al., 2020). Further, our analysis utilizes POLYMOD data, which were collected in the United Kingdom before the onset of the COVID-19 pandemic, for inferring contact patterns for the youngest age group. POLYMOD respondents are not necessarily representative of contact patterns in the United States during our period of interest. Given the relatively low rates of clinical infections and deaths in the youngest age group, any bias in the analyses is likely to be small.
Third, for simplicity and due to lack of data for parameterization, our model does not include waning of immunity from natural infection or from vaccination, although this presents a substantial challenge to the control of COVID-19. Additionally, our implementation of 'leaky' vaccines does not account for reduced symptom severity or reduced probability of transmitting COVID-19. The natural history and epidemiology of future variants may change the landscape of mortality, virulence, and interaction with vaccines. While our analysis is limited in scope to the conditions from the first quarter of 2021, extending this model to the future will need to consider how waning and partial immunity may affect the most effective vaccination strategies for reducing deaths or clinical infections.
Finally, this analysis considers prioritization only by age and worker status and does not include heterogeneity within or between groups. Structural barriers in health care, including financial cost, health complications, and discrimination within the healthcare system -if related to essential worker status -may mean that essential workers face increased health risks in addition to increased contact network size.
There are also likely to be benefits to prioritizing people for vaccination along other socio-demographic axes of risk that are not considered here -especially race, ethnicity, and geographic location -by identifying social inequality itself as a driver of outbreaks (Wrigley-Field et al., 2021;Link and Phelan, 1995). The BICS survey population reflects the composition of the essential workforce in the United States -Blacks and Hispanics comprise of a larger share of the high-contact population (11.12% and 22.49% respectively) relative to their shares in 65+ population (9.12% and 5.04% respectively). Nonetheless, given the strong age gradient in mortality due to COVID-19, the tiered 65+ prioritization strategy averts the most deaths among respondents of all ethnicities (see supplement S1.10), assuming that transmission and mortality are equal by ethnicity and gender within our defined demographic groups (children, HC adults, LC adults, adults 65+). Unfortunately, due to limitations in the sample size we are unable to construct a contact matrix that is disaggregated by age, employment, and race or ethnicity, and thus unable to fully account for heterogeneities across these groups. Although the results of our simulations indicate that relying on indirect effects of prioritizing high-contact workers for vaccination does not ultimately save more lives, high-contact workers may be at increased risk of death compared to other adults because of socio-demographic disadvantage within with the healthcare system not captured within our model. Our analysis supports prioritization of vaccination for the highest risk members of society-which we identify through advanced age, but may instead be a complex combination of socio-demographic disadvantage. This is an important direction for future research.
Overall our results highlight the impact of two dimensions of risk -contact behavior and age-dependent susceptibility and risk of severe disease -on the effect of vaccination strategies. This work also shows the utility of combining mathematical models with detailed contact data by socio-demographic groups, particularly for understanding sensitivity of the effectiveness of different prioritization strategies to the epidemiology of the circulating virus strain. As novel strains are likely to continue to emerge (Brüssow, 2022), these data and models can be especially useful for tailoring prioritization strategies for subsequent outbreaks.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.