key: cord-0285068-5a3sijug
authors: Agarwal, N.; Komo, A.; Patel, C.; Pathak, P. A.; Unver, U.
title: The Trade-off Between Prioritization and Vaccination Speed Depends on Mitigation Measures
date: 2021-02-26
journal: nan
DOI: 10.1101/2021.02.24.21252352
sha: b29f6dd45de6f503dd5e0254caef5afcefb04f73
doc_id: 285068
cord_uid: 5a3sijug

Calls for eliminating prioritization for SARS-CoV-2 vaccines are growing amid concerns that prioritization reduces vaccination speed. We use an SEIR model to study the effects of vaccination distribution on public health, comparing prioritization policy and speed under mitigation measures that are either eased during the vaccine rollout or sustained through the end of the pandemic period. NASEM's recommended prioritization results in fewer deaths than no prioritization, but does not minimize total deaths. If mitigation measures are eased, abandoning NASEM will result in about 134,000 more deaths at 30 million vaccinations per month. Vaccination speed must be at least 53% higher under no prioritization to avoid increasing deaths. With sustained mitigation, discarding NASEM prioritization will result in 42,000 more deaths, requiring only a 26% increase in speed to hold deaths constant. Therefore, abandoning NASEM's prioritization to increase vaccination speed without substantially increasing deaths may require sustained mitigation.

We evaluated disease dynamics for SARS-CoV-2 under vaccine prioritization and mitigation scenarios using an age-stratified SEIR model, building on [9] . Age is a strong correlate of contact rates [10] , susceptibility to infection [11, 12] , and infection fatality rates [13, 14] . Moreover, recommended prioritization rules emphasize age after initial allocation phases [15] . We use eight age bins: 0-9, 10-19, ..., 80+, and incorporate age-specific vaccine efficacy [16, 17] and vaccine hesitancy [18] . We forward simulate the path of the disease for one year starting from estimated initial conditions as of December 14, 2020. The initial number susceptible, infectious, and exposed in each age bin is calculated using death records from [19, 20] . To evaluate the effect of speed, we vary the number of individuals vaccinated per month. The assumptions and parameters of our model are detailed in the supplementary text. We focus on two mitigation scenarios. Sustained Mitigation represents a partiallymitigated pandemic with a basic reproduction number R 0 of 1.5, which corresponds to . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Calibrated Mitigation represents time-varying mitigation measures that keep the total exposed and infectious population no higher than the initial level. Thus, the factor θ is a function of time that fixes R t at 1 until herd immunity is reached. This models a mitigation scenario that loosens measures as the force of infection decreases. It is optimal to vaccinate the elderly under both mitigation scenarios ( Figure 1 ).

In Optimal Prioritization, individuals over the age of 60, who have the highest IFRs and the lowest contact rates, are vaccinated before vaccinating Age 30-59. Vaccinated age groups overlap once a sufficient number of the older people have been vaccinated.

Individuals below the age of 30 are not prioritized even though they have high contact rates.

NASEM's recommendation also prioritizes the elderly, but not as much as the Opti-. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) Although the total incidence is the highest under Optimal Prioritization, it saves the most lives ( Figure 2 ). In both mitigation scenarios, Optimal Prioritization results . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) 

We next evaluate the effect of vaccination speed on reduction of deaths and time to herd immunity relative to an unmitigated pandemic with no vaccinations (Figure 3) . We also consider a No Mitigation scenario with R 0 = 2.6, which is calibrated to estimates in [22] . We consider speeds ranging from 15 million vpm to 40 million vpm. The former corresponds to 1 million doses per day of a two-dose vaccine, which is approximately equal to the rollout speed in the US at the end of the first month [28], to 40 million, which is higher than current Federal government targets [27] .

As expected, the benefits of increasing vaccination speed are large: it decreases both cumulative deaths and time to herd immunity under all scenarios considered.

Increased mitigation also reduces cumulative deaths and delays herd immunity for a fixed vaccination speed and prioritization policy.

The reduction in deaths is larger under NASEM than under No Prioritization for all speeds and mitigation scenarios we considered. By construction, Optimal Prioritization outperforms both. These rankings are reversed for time to herd immunity. The differences between prioritization policies are more pronounced when mitigation measures are less stringent. For each level of speed, cumulative mortality across prioritization policies is most similar under Sustained Mitigation.

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NASEM results in fewer cumulative deaths than No Prioritization for each speed and mitigation scenario considered ( Figure 3 ). However, this ranking may be reversed if . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted February 26, 2021. ; https://doi.org/10.1101/2021.02.24.21252352 doi: medRxiv preprint eliminating prioritization results in higher speed. Figure 4 analyzes this trade-off by reporting the increase in speed needed for No Prioritization to have the same cumulative deaths or YLL as NASEM. We present results varying speed and mitigation scenarios because Figure 3 shows that these two factors influence the effects of a marginal increase in speed. We use an age-stratified SEIR model to benchmark vaccine prioritization policies under different mitigation scenarios. Across the scenarios, vaccinating elderly individuals who have the highest risk first minimizes cumulative deaths even though these individuals have the lowest contact rates (see also [9] ). NASEM guidelines include prioritization for the elderly, but less so than Optimal Prioritization in part due to ethical considerations for healthcare and essential workers [15] . In fact, Optimal Prioritization illustrates that finer age-based prioritization could be valuable even after initial vaccination phases. No Prioritization does not target high-risk individuals, increasing deaths.

Although NASEM reduces deaths relative to No Prioritization, the differences between these policies are significantly smaller if the spread of infections is suppressed by continuing mitigation measures during vaccine distribution. A more realistic mitigation approach that gradually relaxes restrictions during the vaccine distribution results in a larger difference in deaths between NASEM and No Prioritization. Nonetheless, abandoning NASEM may not increase deaths if No Prioritization results in higher vaccination speed. The required gain in speed to keep deaths from increasing is smaller if mitigation measures can be sustained. Thus, combining vaccine prioritization policy with mitigation scenarios in SEIR models is essential for understanding disease dynamics and the health effects of vaccination.

The focal outcomes we study are cumulative deaths and time to herd immunity.

The ranking between the prioritization strategies and the qualitative trade-off between . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted February 26, 2021. ; https://doi.org/10.1101/2021.02.24.21252352 doi: medRxiv preprint speed and prioritization are similar with YLL. However, infection rates are higher and herd immunity is delayed under prioritization policies that reduce deaths. The strain on healthcare capacity or economic costs may weigh in favor of prioritization policies that instead reduce infections. It is possible to adapt our framework to compare the effects of vaccine prioritization and specific mitigation measures on healthcare utilization [31] or economic impacts [24] .

Several states have adapted the NASEM benchmark in devising their own guidelines. Similarly, Calibrated Mitigation is a stylized depiction of the phased approach to restrictions being used in several states. Enriching our framework to more accurately represent vaccine prioritization policies and mitigation scenarios requires more detailed information on these policies. With this information, our model can forecast the interplay between prioritization, mitigation, and speed for particular states.

Our NASEM simulation uses micro data from the US population. Detailed estimates of epidemiological factors that vary by demographics and occupation could be used to further stratify our SEIR model. For instance, contact rates and adherence to mitigation may vary by these characteristics. The model could use such information to more precisely evaluate the effect of prioritizing healthcare workers and first responders in Phase 1A, which represent 5% of the U.S. population. Many guidelines recommend prioritizing these groups partly because of their specific risks and contact rates. Nonetheless, our age-stratified model captures the vast majority of vaccinations occurring after the initial phase.

Our study has several important limitations. Predicting the course of the disease presents challenges for modeling vaccine prioritization policy because of high uncertainty. For example, it is unknown whether recovered individuals have enduring immunity [32] . There are also new strains of SARS-Cov-2, with differing levels of transmissibility and virulence [33, 34] , and vaccine efficacy [35, 36, 37, 38] . How these new strains affect the consequences of vaccine prioritization is unclear. Higher virulence increases the importance of age-based prioritization, vaccination speed, and mitigation.

While our model abstracts away from these new strains, understanding the trade-off . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted February 26, 2021. ; https://doi.org/10.1101/2021.02.24.21252352 doi: medRxiv preprint between prioritization, speed, and mitigation will be necessary for designing effective vaccination and mitigation policies as the disease evolves.

[ . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) gov/nchs/data/nvsr/nvsr68/nvsr68{_}07-508.pdf.

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We use a continuous-time ordinary differential equation (ODE) model with age-stratified We allow susceptible, exposed, and recovered individuals to be vaccinated because differentiating between these groups has not been recommended in the US [15] . However, vaccinations move only susceptible individuals to the (V ) state. Vaccines do not alter the course of individuals already exposed when immunized. We assume that vaccines are transmission blocking if they protect an individual; immunity, if acquired through vaccination, is immediate once the vaccination course has been completed; and no individual can be vaccinated more than once. For two-dose vaccines like the Pfizer-BioNTech and Moderna vaccines, a course is completed only after both doses have been administered.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. We assume that community mitigation scales contact rates proportionally across all groups. Thus, the force of infection for group i at time t is given by

where θ (t) controls the cumulative impact of all community mitigation measures at time t, β i is the transmission probability following a contact with an infectious individual, c ij is the number of daily contacts for individuals in group j that an individual in group i contacts, and I j (t), I X,j (t) and I V,j (t) are the proportions of individuals in group j that are infectious and respectively (i) unvaccinated, (ii) vaccine hesitant, and (iii) vaccinated but unprotected from infection. Thus, the sum of these terms is the probability that an individual in group j is infectious.

We project age-specific contacts rates using data from [10] to the US population to calculate c ij . We use a US-specific contact matrix identifying interactions in all available location types (rural and urban) and settings (home, work, school, and other).

We follow the approach of [9] to collapse 5-year age groups into the 10-year groups in our model. We depart from [9] by using population weights from the ACS. We again follow [9] to extend contact matrices to include individuals aged 80+ by copying the contact rates for individuals aged 70-79 along the diagonal and then adjusting 80+ contact rates to account for long-term care facility interactions. Specifically, contacts between 80+ individuals and 0-60 year old individuals are scaled down by 10% with the amount decreased then evenly redistributed to interactions with 70-79 and 80+ year olds.

The basic reproduction number is R 0 , which is the first eigenvalue of the next-. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted February 26, 2021. ; https://doi.org/10.1101/2021.02.24.21252352 doi: medRxiv preprint generation matrix without mitigation D β CD I , where D β is the diagonal matrix with elements β i , D I is the diagonal matrix with elements d I,i , and C is a matrix with i − j element c ij . We assume that β i is proportional to age-specific susceptibility estimated in [12] (see Table S [42] , we combine estimates from [40] of incubation period and time from symptom onset to death to construct an uncertainty interval of lag of deaths to exposure of 18 to 24 days. We assume that lags are discretely uniformly distributed following [43] . [44] and [45] , our estimates of total true infections are moderately higher. Our estimates are in line with those of [46] and underestimate relative to [47] . Table S.5 compares our age-stratified imputation against the CDC estimates [48] . The CDC estimates are through the end of December while ours are through December 14, 2020. We are therefore unable to directly compare the two true infection estimates. However, the age-distribution of cumulative infections as reported by the CDC closely matches the age-distribution of our total number of infections.

We simulate two types of mitigation scenarios. Sustained Mitigation sets θ (t) = θ 0 for all t, with θ 0 = 1.5/2.6. This value yields an effective reproduction number R t on the initial date of approximately 1.2 since 79.4% of the population is initially susceptible on December 14, 2020 according to our estimates (see Table S .4). The model is equivalent to setting R 0 = 1.5 and evaluating it under no mitigation, that is, θ 0 = 1.

The Calibrated Mitigation scenario sets θ (t) ∈ [0, 1] so that the total exposed plus infectious remains constant until herd immunity is attained. The value of θ (t) is the solution to the problem

where we have combined the compartments E V and E X into E, and I V and I X into I for simplicity of notation. Thus, this sets R t = 1 until herd immunity is attained since the expected number of new exposures caused by a newly infectious individual at time t is equal to 1.

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Time to herd immunity is defined as the earliest date on which the total infectious plus exposed would drop if mitigation measures were lifted:

where we have combined the compartments E V and E X into E, and I V and I X into I for simplicity of notation.

We incorporate vaccine hesitancy by introducing compartments S X , E X , I X and R X . indicating the individual will definitely get the vaccine. The Census age stratification does not match the model group definitions. Thus, we translate their estimates to the model group structure using population weights from the ACS data. Further, consistent with the limitations on the authorization of currently available vaccines, we assume that individuals below the age of 16 cannot be vaccinated [49, 50] . This is incorporated into our model by assuming that their uptake is 0% and thus they are fully hesitant.

The NASEM guidelines define a phased allocation meant to inform vaccine prioritization policy at the federal, state, and local level. They outline five phases (1A, 1B, 2, 3, 4) based on a combination of demographics, individual health risk, and individual occupation. We label each individual in the ACS data to the highest priority NASEM . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted February 26, 2021. ; https://doi.org/10.1101/2021.02.24.21252352 doi: medRxiv preprint phase for which they qualify and simulate an iterative federal to state to individual allocation of vaccines. Federal allocation of incrementally available units to states is by state population share. State allocation of received units to individuals is in NASEM phase order where within-phase allocation proceeds by random lottery. Our phaselabeling procedure follows that of [26] and is outlined below.

Phase 1A includes healthcare workers in high-risk settings and first responders.

We identify these health care workers through industry codes from the ACS data.

NASEM also includes death care professionals, pharmacists, public health workers, and dentists alongside frontline health care workers. These individuals, along with the first responders, are identified using occupation codes. We use the analysis from [51] to only include health care workers in high-risk settings.

Phase 1B includes individuals of all ages with health conditions that put them at significantly higher risk. We use the CDC 2018 Behavioral Risk Factor Surveillance System (BRFSS) dataset to assess risk and merge it with the ACS [52] . For each group defined by age, sex, and race in the BRFSS data, we compute the proportion of individuals with at least two risky health conditions. The BRFSS does not include data on individuals younger than 18, therefore risk probabilities of the youngest agebin with available data, 18-24, are extrapolated to individuals younger than 18. For each observation in the ACS data, we assign individuals to high risk based on the risk probabilities computed from the BRFSS conditional on demographics. Phase 1B also includes older adults living in congregate or overcrowded settings. We identify these individuals in the ACS data by including individuals who are at least 65 years old and live in multigenerational housing or institutional group quarters. Finally, we assign anyone remaining unassigned to Phase 4.

The NASEM guidelines contain approximate estimates of phase sizes. Our phase labeling procedure yields phase sizes that closely match their estimates. Specifically, they specify Phase 1A as 5%, Phase 1B as 10%, Phase 2 as 30-35%, Phase 3 as 40-45%, and Phase 4 as 5-15% of the US population. Our labeling yields Phase 1A as 5%, Phase 1B as 11%, Phase 2 as 37%, Phase 3 as 39%, and Phase 4 as 8% of the US population.

We simulate the model by solving the ODE using a daily discrete-time approximation for 365 days. The pandemic period ends by that time in our simulations. The optimal vaccination policy {V i (t)} i is a function of age-group and time. We solved for this policy using Artleys' KNITRO optimization software. The problem is constrained so that the total daily flow of vaccinated individuals across all groups iVi (t) N i cannot exceed the total number of vaccination courses completed each day. The optimizer . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) 

Figure S.1: Schematic Depiction of the SEIR Model. S X , S V , and S are susceptible; E X , E, and E V are exposed; I X , I, and I V are infectious; R X and R are recovered; D is dead; V is vaccinated and protected. The subscripts X and V denote vaccine hesitant and vaccinated but unprotected respectively.V S ,V E andV R are the rates at which susceptible, exposed and recovered individuals are vaccinated. We ensure that no individual is vaccinated twice by moving individuals from E and R to separate compartments at ratesV E andV R respectively. ν e denotes vaccine efficacy; λ denotes the force of infection; d E and d I are the expected durations in the exposed and infectious states respectively; δ is the IFR.

is initialized at an allocation proportional to the initial population share in each age group.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) Agestratified share of population in each model compartment at start of simulation. S(0) is the share susceptible in the S, S X and S V groups combined; E(0) is the share exposed in the E, E X and E V groups combined; I(0), share infectious in the I, I X and I V groups combined; R(0) is share recovered in the R and the R X groups; D(0) is the share dead.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) [46] estimates are as reported on February 16, 2021. [47] estimates are as reported on December 20, 2020 for their maintain status quo scenario. Our imputation of the percent of US population that has been infected is computed using population counts from the ACS.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) [48] are assumed to include infections occurring through December 31, 2020 whereas our estimates only include infections occurring through December 14, 2020. CDC reported age groups do not align with our group structure.

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