Optimizing vaccine allocation for COVID-19 vaccines: critical role of single-dose vaccination.

Abstract

Most COVID-19 vaccines require two doses, and current vaccine prioritization guidelines for COVID-19 vaccines assume full-dose vaccine deployment. However in the context of limited vaccine supply and an expanding pandemic, policymakers are considering single-dose vaccination as an alternative strategy. Using a mathematical model combined with optimization algorithms, we determined the optimal allocation with one and two doses of vaccine to minimize five metrics of disease burden under various degrees of viral transmission. Under low transmission, we show that the optimal allocation of vaccine critically depends on the level of single-dose efficacy (SDE). If the SDE is high, single-dose vaccination is optimal, preventing up to 36% more deaths than a strategy prioritizing full-dose vaccination for older adults first. With low or moderate SDE, mixed vaccination campaigns with coverage of all older adults with one dose are optimal. However, with modest or high transmission, vaccinating older adults first with two doses is best, preventing up to 41% more deaths than a single-dose vaccination given across all populations. Further, we show that maintaining social distancing interventions and speedy deployment are key for effective vaccination campaigns. Our work suggests that it is imperative to determine the efficacy and durability of single-dose vaccines, as mixed or single-dose vaccination campaigns may have the potential to contain the pandemic much more quickly.

Introduction

COVID-19 has killed over 1,900,000 people worldwide as of January 15, 2021 [1]. With several vaccines proven highly efficacious (estimated at 94.1%, 95% and 62% for Moderna, Pfizer and AstraZeneca, respectively) against COVID-19 disease [2, 3, 4], hopes are high that a return to normal life can soon be possible. Twenty other vaccines are currently in phase 3 clinical trials [5]. Most of these vaccines require two doses given at least three weeks apart [6]. Since a large proportion of the global population needs to be vaccinated to reduce transmission and mortality, vaccine supply shortage will be inevitable in the first few months of vaccine availability. Even in high-income countries, which have secured the largest quantities of vaccine, supply will be initially highly insufficient [7]. This situation could be far worse in low- and middle-income countries (LMIC), where vaccine supplies might arrive at later times and in smaller quantities, with limited vaccine supply for LMIC risking the public and economic health of those populations as well as that of the global population [8].

Most of the current vaccine prioritization schedules use two-dose deployments [9], but the logistics of a two-dose vaccination campaign, which ensures a second dose for those who have already received one dose, are challenging especially in the context of limited vaccine supply and shelf-life [10]. In previous disease outbreaks, fractional dosing, where people receive less than the recommended dosage of vaccine, has been successfully utilized as a way to stretch vaccine supply. A single-dose campaign of the killed oral cholera vaccine (which also requires two doses) was deployed in a recent outbreak in Zambia, where the population was vaccinated with one dose and, months later, high-risk individuals were offered a second dose [11]. In 2016, in response to a yellow fever outbreak in Angola, Uganda and the Democratic Republic of Congo, the WHO vaccinated people with one fifth of the recommended dosage of the yellow fever vaccine [12]. If sufficiently effective, single-dose COVID-19 vaccination is attractive for several reasons: it is easier to implement logistically, potentially less costly, and a larger proportion of the population could be vaccinated in a fixed amount of time, thereby potentially reaching herd immunity levels and allowing resumption of key community activities (e.g., reopening schools, restaurants, gyms, etc.) more rapidly [13, 14, 15]. This may be especially true if vaccines reduce not only COVID-19 disease but also reduce acquisition of SARS-CoV-2 infection and the likelihood of onward transmission; these are open questions and data are still emerging on the full spectrum of vaccine effects [16, 3]. However, the success of a COVID-19 single-dose vaccination campaign depends on the protection acquired after one dose of vaccine. There is an intrinsic trade-off with using single-dose vaccination campaigns to achieve more coverage in exchange for a potentially lower level of protection. In this work, we addressed two questions of public-health importance: 1. Who should be vaccinated first? and 2. How many doses should individuals receive? Utilizing mathematical models combined with optimization algorithms, we determined the optimal allocation of available vaccine doses under a variety of assumptions. We minimized five metrics of infection and disease burden: cumulative infections, cumulative symptomatic infections, cumulative deaths, and peak non-ICU and ICU hospitalizations. We showed that mixed vaccination strategies in which some age groups receive one dose while others receive two doses can achieve the greatest reduction in these metrics under fixed vaccine quantities. Further, our results suggest that the optimal vaccination strategy depends on the relative efficacy of single- vs. full-dose vaccination; on the full spectrum of vaccine effects; on the number of vaccine doses available; and on the speed of vaccine rollout and the intensity of background transmission.

Results

We built upon our previous model of SARS-CoV-2 dynamics and vaccination [17]. Briefly, we developed an age-structured mathematical model with the population of Washington state (7.6 million people) and US demographics divided into 16 age-groups [18] (Fig. S1). To perform the vaccine optimization, we collapsed the 16 age-groups into 5 vaccination age-groups: 0–19, 20–49, 50–64, 65–74 and those 75 and older, aligned with vaccination groups currently considered by the Centers for Disease Control and Prevention (CDC) [19]. We assumed that at the beginning of our simulations, 10% of the population has been infected and is immune [20] (alternative scenario: 20% see Sensitivity Analysis, SI). We assumed that asymptomatic and symptomatic infections are equally infectious (alternative scenario: Sensitivity Analysis, SI) and confer complete immunity upon recovery. Further, we assumed that both naturally-acquired immunity and vaccine-induced immunity (one- and two-dose) are long-lasting, so that there is no waning during the time period analyzed.

Because it is expected that vaccine supplies will ramp up considerably over the second half of 2021 and into 2022, we focused on the first few months of vaccine availability and set 6 months for the duration of our simulations. We considered the distribution of enough vaccine doses to cover from 10% to 50% of the population with a single dose. We simulated vaccination campaigns delivering 150,000 (150K) vaccine doses per week, with a maximum of 50% of the population vaccinated with a single dose of vaccine over a ~6-month period (our time horizon). This matches current vaccination plans in the US [21]. An alternative scenario with 300K vaccine doses per week was also explored. These are roughly twice and four times, respectively, the vaccination rate experienced in the US during the 2009 H1N1 influenza pandemic [22].

We considered four levels of background SARS-CoV-2 transmission, resulting in an effective reproductive number (defined as the average number of secondary cases per infectious case in a population made up of both susceptible and non-susceptible hosts) of R_eff = 1.2, 1.4, (currently observed in WA state, [23]), 1.7 or 3 that was kept constant over time. We assumed that front-line workers (e.g., healthcare workers, firefighters), who should be prioritized, have already been vaccinated, and they are not explicitly modeled here. We evaluated five metrics of disease and healthcare burden: cumulative infections, cumulative symptomatic infections, cumulative deaths, maximum number of non-ICU hospitalizations and maximum number of ICU-hospitalizations. State goals for limiting hospital and ICU beds occupied by COVID-19 patients [24, 25] were used for result interpretation.

Ongoing phase 3 COVID-19 vaccine trials evaluate vaccine efficacy against laboratory-confirmed COVID-19 disease, or the multiplicative reduction in per-exposure risk of disease which we denote by VE_DIS. We considered a leaky vaccine (that is, a vaccine that confers partial protection to all vaccinated individuals) that can have three effects on vaccinated individuals [26]: reducing the probability of acquiring a SARS-CoV-2 infection (measured by VE_SUS), reducing the probability of developing COVID-19 symptoms after infection (measured by VE_SYMP), or reducing the infectiousness of vaccinated individuals upon infection (measured by VE_I, Fig. S2A).

Given the efficacy data on two-dose COVID-19 vaccines to date [2, 3, 4], we considered a main scenario with VE_DIS = 90%. Because many combinations of VE_SUS and VE_SYMP can result in the same VE_DIS (Fig. S2B), and in advance of definitive data on VE_SUS or VE_SYMP for COVID-19 vaccines, we considered three different vaccine profiles that yield VE_DIS = 90%: a vaccine effect mediated by VE_SUS only, a vaccine effect mediated by VE_SYMP only, and a vaccine effect that is a combination of VE_SUS and VE_SYMP (Fig. S2B, table S1). In the absence of data on the vaccine effect on infectiousness, we took a conservative approach and assumed VE_I = 0 (alternative scenario, VE_I = 70%, Sensitivity Analysis, SM). Given the limited data to-date regarding the efficacy of single-dose vaccination, we considered three “single-dose efficacy” (SDE) scenarios, under our main scenario where two-dose VE_DIS = 90%: low SDE, whereby the single-dose vaccine confers low efficacy against COVID-19 disease (${\text{VE}}_{{\text{DIS}}_1}=18\%$); moderate SDE with ${\text{VE}}_{{\text{DIS}}_1}=45\%$; and high SDE with ${\text{VE}}_{{\text{DIS}}_1}=72\%$; corresponding to 20, 50, and 80% of the 90% efficacy of the full two-dose regimen, respectively. The efficacy of single-dose vaccination against infection and symptoms were assumed to be reduced proportionally. All vaccine effects were assumed to take effect immediately following the last vaccination and to be constant over the time horizon of 6 months. For two dose vaccination, we explicitly modeled vaccination campaigns with the first dose, followed by vaccination campaigns with the second dose, so that individuals receiving two doses had the protection conferred by single dose vaccination in the inter-vaccination period.

Throughout the text, we refer to vaccine coverage as the amount of vaccine available to cover a percentage of the population with one dose of vaccine. For each vaccination scenario and disease metric, we compared the optimal allocation strategy that minimized the respective disease metric (as determined by our optimization routine) to two other strategies: a pro-rata strategy in which one-dose vaccination is rolled out across all age groups proportional to their size; and a high-risk strategy in which two-dose vaccination is rolled out to the oldest age group first and then to younger age groups in decreasing order as vaccine availability permits (similar to the current prioritization strategy in the US [27]). For example, with 20% coverage, under the pro-rata strategy 20% of each group would receive a single dose of vaccine, and under the high-risk strategy all people aged 75 and older and 32% of those aged 65 to 74 years would receive two doses of vaccine (Fig. S3)A.

In the main scenario, we considered a vaccine mediated both by VE_SUS and VE_SYMP, so that VE_DIS = 90% after two doses with VE_SUS = 70% and VE_SYMP = 66%, a vaccination campaign with 150K doses per week, and R_eff = 1.4, focusing on minimizing COVID-19 deaths.

Single dose vaccination strategies are optimal if SDE is high.

If a limited number of vaccine doses are available (≤ 20% coverage) then for all metrics considered, the optimal strategies allocated vaccines to children and younger adults (who are the high-transmission groups in our model), regardless of the efficacy of a single dose (Fig. 1A–F and Fig. S4).

Figure 1: Optimal vaccine allocation strategies for minimizing deaths for different vaccination coverages.

For each plot, the bars represent the percentage of each age group vaccinated with a single dose (light blue) and two-doses (dark blue) when there is enough vaccine to cover 10% to 50% (as indicated by row) of the population with a single dose. The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively.

If SDE was low or moderate combined with low coverage, the optimal strategies allocated two doses of vaccine to the high-transmission groups Fig. S3A and B), averting up to 45 and 25% more deaths compared to the high-risk and pro-rata strategies (low SDE, 20% coverage, Fig. 2D and E). This is because at low coverage, the most effective strategy is to reduce the transmission as much as possible, and this is achieved by prioritizing vaccination of the most active groups (Fig. S3D and E). For higher coverage (30–50%), mixed allocation strategies were optimal, vaccinating all age groups with two doses and additionally vaccinating older adults with a single dose to boost their coverage (Fig. 1G, H, J, K, M and N). For example, with 50% coverage, 25, 20, 10, 10, and 28% of each age group was vaccinated with two doses, and an additional 19, 32 and 47% of the 50–65, 65–75 and 75+ were vaccinated with a single dose (Fig. 1M). Here, the optimal strategy averted up to 40% more deaths than the pro-rata strategy, but performed similarly to the high-risk strategy (9% more deaths averted for 30% coverage and moderate SDE, Fig. 2D and E).

Figure 2: Percentage of deaths averted for different levels of SARS-CoV-2 transmission.

Percentage of deaths averted for the optimal allocation strategies (blue), the high-risk strategy (pink) and the pro-rata strategy (green) with enough vaccine to cover 10–50% of the population with one dose. Each row represents a different level of SARS-CoV-2 transmission resulting in R_eff = 1.2 (A-C), 1.4 (D-F), 1.7 (G-I) or 3 (J-L). The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively. Shaded areas represent results of 1,000 parameter simulations with the top and bottom 2.5% removed.

In sharp contrast, if a single dose of vaccine was highly efficacious, then, for all metrics considered, the optimal strategies involved vaccinating individuals with one dose of vaccine almost exclusively (Fig. 1, Figs. 3 and S4 panels C, F and I). If the vaccine supply was limited (up to 20% coverage), it was optimal to allocate a single dose of vaccine to the high-transmission groups, averting up to 36 and 11% more deaths than the high-risk and pro-rata strategies (10% coverage, Fig. 2F). For higher coverage (30–50% coverage) the pro-rata strategy was in fact optimal (Fig. 4C), averting 13–26% more deaths than the high-risk strategy. If sufficient doses of high SDE vaccine were available to ensure 50% coverage, this strategy significantly mitigated the epidemic by preventing 78% of the expected COVID-19 deaths over 6 months (compared with no vaccination, Fig. 4F).

Figure 3: Optimal vaccine allocation strategies for different disease metrics with 50% coverage.

Optimal vaccine allocation for a vaccine with VE_DIS = 90% and assuming enough vaccine to cover 50% of the population with a single dose (25% with two doses). Each row represents a different disease metric minimized: cumulative infections (A-C), cumulative symptomatic infections (D-F), non-ICU peak hospitalizations (G-I), ICU hospitalizations (J-L) and total deaths (M-O). The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively.

Figure 4: A-C: Optimal pro-rata and high-risk allocation strategies with 50% coverage.

Optimal (light and dark blue), high-risk (pink) and pro-rata (green) allocation strategies assuming enough vaccine to cover 50% of the population with a single dose (25% with two doses). Within each panel, the bars represent the percentage vaccinated in each vaccination group. D-E: Prevalence of symptomatic infections. Prevalence of symptomatic infections (per 100,000) in the absence of vaccine (black), with the optimal allocation strategy to minimize deaths (blue), the high-risk strategy (pink) or the pro-rata strategy (green) with enough vaccine to cover 50% of the population with a single dose (25% with two doses). The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively.

Different metrics have different optimal allocation strategies.

Minimizing other metrics of disease and healthcare burden produced different optimal allocation strategies. With low coverage, regardless of the value of the SDE, the optimal allocation was similar across metrics with all vaccine doses was designated to the high-transmission groups (children and young adults) (Fig. S4). With higher coverage and high SDE, it was best to allocate vaccine to high-transmission groups to minimize transmission (cumulative infections and symptomatic infections, Fig. 3C and F), but it was best to allocate vaccine with a pro-rata strategy to minimize severe disease outcomes (hospitalizations and deaths, Fig. 3I, L, O). Notably, with 50% coverage, the optimal and the high-risk strategies maintained the number of peak ICU hospitalizations below total capacity, but only the optimal strategy achieved the Washington state goal for non-ICU peak hospitalizations (Fig. S5 and Fig. S6).

Rapid vaccination roll-out under sustained social distancing is key for successful vaccination campaigns.

We investigated the effect of SARS-CoV-2 transmission on optimal allocation strategies. Under stringent social distancing interventions maintaining R_eff = 1.2, the efficacy after a single dose determined the optimal allocation strategy. With low or moderate SDE and low coverage, it was optimal to vaccinate high-transmission groups with two doses. If SDE was low, the optimal strategy averted 34 and 35% more deaths than the high-risk and pro-rata strategies respectively (10% coverage, Fig. 2A). With higher coverage, mixed strategies were optimal, with adults aged 50–74 being vaccinated in a higher proportion with a single dose (Fig. 5A, B, D, and E); with 50% coverage, the optimal strategy averted 12% and 40% more deaths than high-risk and pro-rata strategies respectively (Fig. 2B). If the SDE was moderate, the optimal strategy averted 35 and 18% more deaths than the high-risk and pro-rata strategies at low coverage, but only averted an additional ~12% more deaths than the other two strategies at high coverage. In contrast, if the vaccine had high SDE, the pro-rata strategy was in fact optimal for all coverages, averting additional 40% deaths than the high-risk strategy at low coverage and 18% at high coverage (Fig. 5C and F, Fig. 2C).

Figure 5: Optimal vaccine allocation for minimizing deaths for different levels of SARS-CoV-2 transmission and 50% coverage.

Optimal vaccine allocation for minimizing deaths with a vaccine with VE_DIS = 90% and assuming enough vaccine to cover 50% of the population with one dose (or 25% with two doses). For each panel (A-L), the bars represent the total percentage of the population in each vaccination group to be vaccinated, split in those receiving one dose (light blue) and those receiving two doses (dark blue). Each row represents a different level of SARS-CoV-2 transmission resulting in an R_eff = 1.2 (A-C), 1.4 (D-F), 1.7 (G-I) or 3 (J-L). The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively.

If viral transmission was moderate or high (R_eff = 1.7 or 3), then the high-risk strategy was the optimal use of vaccine especially for scenarios with low and moderate SDE, where it averted up to 41% more deaths than the pro-rata strategy (R_eff = 1.7, 40% coverage and low SDE, Fig. 5 and Fig. 2G, H, J, K). For high SDE, the optimal strategy was still to vaccinate the high-risk groups first, but using mixed vaccination (with one and two doses). For example, with enough vaccine to cover 50% of the population and a vaccine with a high SDE, it was optimal to cover all adults aged 65 and over with two doses and those aged 50–64 with a single dose of vaccine with the remaining vaccine supply (Fig. 5I and L). However, the gain from optimizing vaccine allocation to improve high-risk strategy was relatively small at low coverage (10% more deaths averted with 20% coverage), but averted up to 20% more deaths than the pro-rata strategy (10% coverage, R_eff = 3). All strategies performed similarly for high coverage (Fig. 2I and L).

Regardless of the SDE, for all levels of viral transmission considered, the epidemic advanced at a faster pace than the vaccination campaign, evidenced by the fact that the percentage of deaths averted plateaued at 40% (R_eff = 1.2) and 30% coverage (R_eff = 1.4, 1,7 and R_eff = 3), Fig. 2. Notably, in controlled epidemic settings (R_eff = 1.2 and 1.4) the optimized strategies allow for reaching the ceiling of the vaccination impact much faster with significantly fewer vaccine doses.

The vaccine profile shapes the optimal allocation strategy.

In this section we analyzed how different vaccine profiles affected the optimal allocation strategies. With a vaccine effect on COVID-19 disease mediated by a reduction in symptoms (high VE_SYMP), the optimal strategies for minimizing deaths allocated two doses of vaccine to older adults (aged 65 and older) for direct protection (Fig. 6A–C). If the reduction in disease was mediated by both a reduction in SARS-CoV-2 infection and in symptoms (high VE_SYMP and VE_SUS), or predominately by preventing infection (VE_SUS), then mixed strategies allocating more vaccine doses to older adults are optimal for a low or moderate SDE while the pro-rata strategy was optimal if the SDE was high (Fig. 6D–I).

Figure 6: Optimal vaccine allocation to minimize deaths for different vaccine profiles with 50% coverage.

Optimal vaccine allocation for minimizing deaths for a vaccine with VE_DIS = 90% and assuming enough vaccine to cover 50% of the population with a single dose (25% with two doses). For each panel (A-I), the bars represent the total percentage of the population in each vaccination group to be vaccinated, split in those receiving a single dose (light blue) and those receiving two doses (dark blue). Each row represents a different breakdown of VE_DIS = 90% as a function of VE_SUS and VE_SYMP. Top row (A-C): VE_DIS is mediated by a reduction in symptoms upon infection. Middle row (D-F): VE_DIS is mediated by a combination of reduction in susceptibility to infection and reduction of symptoms upon infection. Bottom row (G-I): VE_DIS is mediated by a reduction in susceptibility to infection. The columns correspond to assumptions that the single-dose efficacy (SDE) is low (left column, ${\text{VE}}_{{\text{DIS}}_1}=18\%$), moderate (center column, ${\text{VE}}_{{\text{DIS}}_1}=45\%$) or high (right column, ${\text{VE}}_{{\text{DIS}}_1}=72\%$), corresponding 20, 50 or 80% of the 90% efficacy that is assumed following two doses of vaccine, respectively.

The vaccine efficacy profile had little effect on mortality prevented by the high-risk strategy (regardless of the SDE) but a major effect on the pro-rata strategy impact: while this allocation performed very poorly if the vaccine was mediated by VE_SYMP and low SDE, it was extremely effective if the vaccine was mediated also by VE_SUS and had a high SDE (Fig. S7). A vaccine preventing only symptomatic disease has the potential to prevent only up to 62% of deaths over 6 months compared to 86% reduction in mortality if exclusively mediated by preventing infection (Fig. S7C and I). Moderate protection against infection (VE_SUS) was important to all vaccination strategies to ensure reduction in transmission but especially for the optimal strategy (Fig. S8). A vaccine acting exclusively by reducing symptomaticity had no impact on the overall transmission (maximum of 4% of cumulative infections averted, Fig. S8A–C) while a vaccine that reduced SARS-CoV-2 acquisition could, if optimally allocated, avert 97% of cumulative infections (Fig. S8I).

Sensitivity analysis

Results assuming asymptomatic infections are less infectious:

Simulations assuming that asymptomatic infections are 50% less infectious than symptomatic infections showed similar results. The optimal allocation strategies in this scenario depended mostly on the SDE, notably: i) the pro-rata strategy was optimal for high SDE and high coverage and ii) single-dose vaccination of the high transmission groups was the optimal strategy with low coverage (Fig. S9). As expected, if asymptomatic infections are less infectious, then a vaccine mediated exclusively by reducing symptomatic disease does have a significant impact in overall transmission, preventing as much as 66% of total infections (50% coverage, high SDE, Fig. S10). Furthermore, under this scenario, such a vaccine would avert slightly more deaths (a maximum of 67% averted deaths vs 63% in the main scenario).

Results assuming 20% cumulative incidence at the start of vaccination:

We repeated the main analysis assuming 20% of the population has been infected and therefore immune at the beginning of vaccination. Again, the results were consistent with the main scenario, with optimal vaccination strategies favoring single-dose campaigns if the SDE is high (Fig. S11). In this scenario, the epidemic grows very slowly even in the absence of vaccine with only the exponential phase of the epidemic curve observed toward the end of the simulations. This is because with 20% of the population already immune and the assumed reduction in contacts resulted in an much lower R_eff (R_eff = 1.2). As a result, the projected impacts of different strategies are very similar to the ones presented above with R_eff = 1.2 with optimal strategy outperforming the other strategies for low and moderate SDE and pro-rata strategy being optimal for high SDE (Fig. S12).

Results assuming more rapid vaccine delivery:

We next investigated the effect of vaccination rate in the optimal allocation strategies. Here, we assumed that vaccine was rolled out at 300K doses per week (twice as fast as main scenario). At this rate, 100% of the population can be vaccinated with a single dose in the same time period. With low coverage, the optimal strategy was identical to the one described in the main scenario. With high coverage, the optimal strategy differed only for low and moderate SDE, by allocating even more vaccine with two doses to the high-transmission groups (Fig. S13D, E). With enough vaccine to cover 50% of the population and administering 300K doses per week the optimal strategy averted 17% more deaths compared to one distributing 150K doses per week (95% and 78% the deaths averted compared with no vaccination, vaccinating at 300K and 150K doses per week respectively, Figs. S13C and 4E). Furthermore, at this rate, the optimal strategy significantly mitigates transmission even with low and moderate SDE, and temporary herd immunity is achieved if the vaccine has a high SDE (Fig. S13G–I).

Results assuming vaccine efficacy in reducing infectiousness upon infection:

We identified the optimal allocation strategies assuming that a vaccine, in addition to all the effects previously described (VE_DIS = 90% after two doses with VE_SUS = 70% and VE_SYMP = 66%) also reduces infectiousness upon infection by 70% (VE_I = 70%) after two doses. For low and high SDE and for all coverage levels considered, the optimal strategies were very similar to the ones previously described. For moderate SDE the optimal allocation suggested more single dose vaccination of the high-transmission groups at low coverage, and mixed vaccination of all age groups for high coverage, reducing the focus on older age groups (Fig. S14). As expected, all vaccination strategies averted more deaths due to additional vaccine effects on infectiousness. With 50% coverage, the optimal strategies averted 10% more deaths compared to the main scenario, regardless of the SDE (74, 80 and 88% deaths averted for low, moderate and high SDE in this scenario vs. 64, 69 and 78% deaths averted for the main scenario, Figs. 4 and S15 panels A-C).

Discussion

COVID-19 vaccination has begun in several countries, and more countries will start in the upcoming months. As demand will far exceed supply in the initial months of vaccine deployment, vaccine will need to be prioritized. Most of the current strategies consider vaccination with full dosage (two doses), but some countries have proposed vaccinating twice as many people with a single dose (and delaying the second dose) [28]. An intense debate about how best to use the available vaccine is ongoing [13, 29, 30]. Here, we show that there is no universal answer to this question. Pairing a mathematical model parameterized using the evidence to-date on the efficacy of COVID-19 vaccines with optimization algorithms, we explore the use of single-dose campaigns and mixed vaccination campaigns, with some people receiving one dose and others receiving two doses, and we find that the optimal use of resources depends primarily on the level of single-dose efficacy, in agreement with [15]. If a single dose of vaccine is highly efficacious and introduced under stringent social distancing interventions with low viral transmission, our results suggest that campaigns that optimally distribute a single vaccine dose to more people are far more effective at averting deaths than a two-dose vaccination campaign prioritizing subpopulations at high risk of COVID-19 severe disease and death. Previous work for other infectious diseases [31, 32, 33] has reached similar conclusions. Furthermore, our results show that vaccinating with a single-dose at a faster rate could result in temporary herd immunity, in agreement with previous work [34]. As more vaccine becomes available, additional vaccination campaigns will be needed to cover everyone with the full two doses of vaccine. However, in places where SARS-CoV-2 transmission is moderate or high (R_eff = 1.7 or 3 in our model), a two-dose campaign from the outset is optimal.

In addition, we show that optimal distribution of available vaccine doses across subpopulations depends strongly on the level of transmission. If the ongoing transmission in the community is well controlled with stringent non-pharmaceutical interventions in place, the optimal strategy allocated vaccine to the high-transmission groups, consistent with previous work [35]. If the transmission is moderate or high, it is optimal to directly protect those at higher risk of severe disease and death, also in agreement with previous results [36, 17]. Our analysis reiterates the absolute necessity of maintaining social distancing throughout vaccination [37, 38, 39]: if social distancing interventions are lax before vaccination is advanced, or if vaccination is not rolled out fast enough, then the current epidemic wave will be over long before vaccination campaigns are completed and the effect of vaccination will be limited.

While high vaccine efficacy against COVID-19 disease has been reported for the two licensed vaccines (Pfizer and Moderna), other effects of COVID-19 vaccines require further evaluation, including their effects on preventing SARS-CoV-2 infection and on infectiousness. To account for these gaps in knowledge, we investigated the optimal vaccine allocation under three possible vaccine profiles consistent with the observed vaccine efficacy against disease, and we found that the optimal vaccination strategy depends on the profile. Our analysis showed that a vaccine which mostly mitigates symptoms but does not reduce the risk of infection should be prioritized to the oldest age groups at full dosage. In contrast, the optimal strategy for a vaccine which provides at least moderate protection against infection includes more balanced dose distribution across age groups with larger proportions assigned to one-dose vaccinations. Similar to [39], we found that a vaccine that only prevents disease upon infection will have limited population impact, whereas a vaccine preventing infection will both reduce population transmission and subsequent morbidity and mortality. These results underscore the need for thorough studies to evaluate all of the vaccine effects.

Beyond the impact on infection and disease burden, there are additional arguments for considering single-dose vaccination, including greater equity achieved in distributing a scarce commodity (vaccine) [13], reduced reactogenicity following the first versus the second dose of the mRNA vaccines [16, 3], and the potential for greater population uptake and adherence to a single-dose regimen. Policy-makers would ideally consider these issues in evaluating possible vaccination strategies.

Here, we report the optimal use of resources as determined by mathematical optimization. In practice, other factors (ethical, political, logistical, etc.) need to be considered when allocating vaccine. We quantified the advantages and disadvantages of two policies that closely mimic current guidelines—pro-rata vaccination and vaccination of groups at high risk of disease— and identified when either of these coincides with our computed optimal allocation strategy, or achieves similar public health impact. While optimal allocation strategies may be difficult to implement, our results can be used to guide the development of mixed vaccination strategies, where some subpopulations receive one dose and others receive two doses, thereby achieving a balance between rapid coverage and full protection of those most at risk of severe disease and death.

Our work has several limitations. Our model assumed that asymptomatic and symptomatic infections confer equal protection, but asymptomatic infections could result in weaker protection [40]. We assumed that naturally and vaccine-induced immunity will be long-lasting, but some studies suggest that it might last only a few months [41]. Ongoing phase 3 trials will establish the durability of vaccine efficacy, with participants followed 1 to 2 years post-last vaccination. If immunity is short-lived, then our results are valid only for that time frame. We also assumed that vaccinating previously infected individuals would have no effect on their immunity. However, it is possible that previous infections might act as a first dose of vaccine and that vaccinating those individuals might result in a boost of their immunity. We use age-stratified hospitalization rates based on data from Wuhan, China [42] and mortality rates based on data from France [43]. These rates strongly depend on comorbidities (e.g., heart disease, diabetes, etc.) that are country-dependent. It is then important to determine country-based estimates of these rates to adequately parameterize models. For mathematical and computational tractability, we used a deterministic model that does not account for geographic movement or complex contact patterns and age was our sole risk factor. In reality, we know that other factors, such as occupation, have been linked to an increased risk of acquisition and severe disease [44, 45]. Because of systemic social inequalities, several studies have shown that in certain countries people from racial and minority groups are at increased risk of infection and death from COVID-19 [46]. Further, deterministic models can overestimate infection dynamics. While comparisons with and without vaccination strategies would not be affected by this, is possible that our peak hospitalizations are overestimated. We kept the effective reproductive number (and hence viral transmission) constant throughout the simulations. However, social distancing interventions are being constantly changed and adapted to new challenges when transmission is high. We included children in our analysis, but vaccines are not currently licensed for individuals under 16 years old. However, studies are currently undergoing for the AstraZeneca and Pfizer vaccines including children 12 years old and older [47] and studies in children for other vaccines are being planned, so it is possible that one or more COVID-19 vaccines will be licensed in children within the next 6 months. Finally, we have determined optimal allocation strategies in the context of considerable uncertainty as to COVID-19 vaccine profiles and vaccine rollout; once profile, vaccination rates and coverages for specific countries are known, we welcome validation with more complex models.

There are reports of new and more transmissible SARS-CoV-2 variants originating from the UK and South Africa that are spreading rapidly and circulating in several parts of the globe. It is still unknown how efficacious currently available vaccines will be against these variants [48, 49]. A potential concern with single-dose vaccination is that vaccinating large numbers of people with a regimen with suboptimal efficacy may allow selection to drive the emergence of new vaccine-resistant variants that can rise rapidly in frequency [50].

While limited data suggest that a single dose of the three COVID-19 vaccines with regulatory licensure or approval in the US and UK might confer high efficacy [2, 3, 51], the data are preliminary and the duration of protection is unknown. Other vaccines that require two doses, such as the oral cholera vaccine, are highly effective after a single dose but the protection provided is short-lived compared to that provided by the full two-dose regimen [52]. If single-dose immunity lasts for at least 6 months, our results show that single-dose vaccination campaigns, which are much easier to implement, are the optimal use of resources in the short term, with the goal to fully vaccinate the entire population in the long term. In the absence of phase 3 efficacy data on single-dose vaccination, it will be crucial for vaccine safety systems to capture any breakthrough infections that occur among individuals receiving vaccination under population campaigns—especially those receiving a single dose; and for longitudinal immune responses to be measured in clinical trial participants who received only one dose. Our work suggests that it is an absolute imperative to quickly and fully determine the peak and duration of efficacy of single-dose vaccinations, as these data are needed to support further investigation of mixed vaccination campaigns which have great potential to more quickly contain the pandemic.