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

Abstract

Most COVID-19 vaccines require two doses, and current vaccine prioritization guidelines for COVID-19 vaccines assume two-dose vaccine deployment. However in the context of limited vaccine supply and an ongoing pandemic, policymakers are considering single-dose vaccination as an alternative strategy. Using a mathematical model combined with optimization algorithms, we determined optimal allocation strategies 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 vitally depends on the level of single-dose efficacy (SDE). If the SDE is high, single-dose vaccination is optimal, preventing up to 22% more deaths than a strategy prioritizing two-dose vaccination for older adults. With low or moderate SDE, mixed vaccination campaigns with complete coverage of older adults 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 adult 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 2,400,000 people worldwide as of February 21, 2021 [1]. With several vaccines proven highly efficacious (estimated at 94.1%, 95%, 82% and 91.6% for Moderna, Pfizer and AstraZeneca, and Sputnik V respectively) against COVID-19 [2, 3, 4, 5], hopes are high that a return to normal life can soon be possible. Twenty other vaccines are currently in phase 3 clinical trials [6]. Most of these vaccines require two doses given at least three weeks apart [7]. 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 highly insufficient initially [8]. 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 [9].

Most of the current vaccine prioritization schedules use two-dose deployments [10], 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 [11]. In previous outbreaks of other infectious diseases, 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 cholera outbreak in Zambia, where the population was vaccinated with one dose and, months later, high-risk individuals were offered a second dose [12]. In 2016, in response to a yellow fever outbreak in Angola, Uganda and the Democratic Republic of Congo, a vaccination campaign with one fifth of the recommended dosage of the yellow fever vaccine [13] was successfully carried out [14, 13]. 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 [15, 16, 17]. This may be especially true if COVID-19 vaccines not only reduce disease but also prevent infection and hence onward transmission; these are open questions and data are still emerging on the full spectrum of vaccine effects [18, 3, 19]. 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 achieving greater vaccine coverage, in exchange for a potentially lower level of protection and/or less durable 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, and at levels of vaccine efficacy consistent with estimates from phase 3 efficacy trials. We independently minimized five metrics of infection and disease burden: cumulative infections, cumulative symptomatic infections, cumulative deaths, and peak non-ICU and ICU hospitalizations. The last two metrics were chosen as way to evaluate healthcare system burden. We showed that mixed vaccination strategies in which some age groups receive one dose while others receive two doses can achieve the greatest reductions in these metrics under fixed vaccine quantities. Further, our results suggest that the optimal vaccination strategy depends on the relative efficacy of single-versus 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. This highlights the critical importance of continued research to define the level of efficacy conferred by a single vaccine dose and to evaluate efficacy against not only COVID-19 disease, but SARS-CoV-2 infection and secondary transmission.

Results

Because it is expected that vaccine supplies will ramp up considerably over the second half of 2021 and into 2022, and because there is considerable uncertainty around durability of vaccine protection, we focused on the first few months of vaccine availability and set 6 months for the duration of our simulations. We built upon our previous model of SARS-CoV-2 transmission and vaccination [20]. 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 [21] (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) [22]. We assumed that at the beginning of our simulations, 20% of the population of pre-existing immunity [23], and the SARS-CoV-2 prevalence (number of current SARS-CoV-2 active infections) is 0.1% of the population [24] (alternative scenarios: 10% pre-existing immunity and 0.05% or 0.3% prevalence, see Sensitivity Analysis, SI). We assumed that asymptomatic infections are 75% as infectious than symptomatic infections (alternative scenario: 30% as infectious, see Sensitivity Analysis, SI) and confer complete immunity upon recovery, over our time horizon of 6 months. Further, we assumed that both naturally-acquired immunity and vaccine-induced immunity (one- and two-dose) do not wane during our 6 month time horizon.

We considered four levels of background SARS-CoV-2 transmission, resulting in effective reproductive numbers (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 = 1.1 (observed in WA state in January 2021 [25]), 1.3, 1.5 and 2.4, respectively, at the beginning of our simulations. Of course, as vaccination and the epidemic process progress, the R_eff will change. 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 [26, 27] were used for result interpretation.

Modeling the vaccine effects

Ongoing phase 3 COVID-19 vaccine trials evaluate vaccine efficacy against laboratory-confirmed COVID-19, 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 [28]: to reduce the probability of acquiring a SARS-CoV-2 infection (measured by VE_SUS), reduce the probability of developing COVID-19 symptoms after infection (measured by VE_SYMP), or reduce 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, 29, 3, 30], 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 1). 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 of vaccines intended to be given in a two-dose schedule [31, 4], 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 $\left({\text{VE}}_{{\text{DIS}}_1}=18\%\right)$; 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 each vaccine dose and to remain constant after the last vaccine dose 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.

Table 1:

Description of vaccine efficacies used in the model.

Modeling vaccination campaigns

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 [32]. An alternative scenario with 300K vaccine doses per week was also explored (Sensitivity Analysis). These are roughly twice and four times, respectively, the vaccination rate experienced in the US during the 2009 H1N1 influenza pandemic [33].

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 denote the optimal strategy as the allocation that was found to minimize a given disease metric, as determined by our optimization routine. We compared the optimal strategy to two other strategies: a pro-rata strategy in which one-dose vaccination is rolled out across all adult age groups proportional to their population size; and a high-risk strategy in which two-dose vaccination is allocated to the oldest age groups first and then to younger age groups in decreasing order as vaccine availability permits (similar to the current prioritization strategy in the US [34]). For example, with 50% vaccine coverage, under the pro-rata strategy 66.5% of each age group (excluding children) would receive a single dose of vaccine, and under the high-risk strategy all of those aged 65 and older and 44% of those aged 50 to 64 years would receive two doses of vaccine (Fig. S3). We also compared the optimal strategy to a pragmatic strategy, where all adults aged 65 and older receive two doses of vaccine and all other adults receive a single dose as coverage permits. The results for this strategy were nearly identical to those from the high-risk strategy , so we present only the latter set of results. For each of these strategies and for each outcome, we then ran the model with 1,000 different parameter sets and removed top and bottom 2.5% of the simulations to calculate uncertainty intervals (denoted below as 95% UI) reflecting the uncertainty in the outcomes arising from uncertainty in the parameter estimates (Uncertainty analysis, SM).

In the main scenario, we considered R_eff = 1.1, 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, focusing on minimizing COVID-19 deaths.

Results assuming low background viral transmission.

In this section, we assumed that vaccination started under a low background transmission, resulting in an R_eff = 1.1 or R_eff = 1.3, as experienced in WA state in January 2021 [25]. For low SDE combined with low vaccination coverage (enough vaccine to cover up to 20% of the population with a single dose), the optimal strategy allocated two doses of vaccine to the high-transmission group (adults aged 20–49 in our model) and the high-risk groups (adults aged 65 and older, Figs. 1A, D and 2A). The optimal strategy averted up to 37% more deaths compared to the pro-rata strategy (R_eff =1.3 and 20% coverage with a single dose, optimal: 54% (95% UI: 51–55) vs. pro-rata: 16% (95% UI: 12–19) deaths averted compared with no vaccination) and 12% more deaths compared to the high-risk strategy (R_eff =1.1 and 10% coverage, optimal: 42% (95% UI: 35–45) vs. high-risk: 30% (95% UI:27–31)), Fig. 3A and D. Even at low coverage, the optimal strategy to minimize deaths also resulted in a significant reduction in overall transmission (Fig. 2D). As coverage increased, the optimal strategy prioritized coverage in older adults with two doses of vaccine (Fig. 1G, J and M), averting over 34% more deaths than the pro-rata strategy , with a maximum of 45% more deaths averted (R_eff =1.3, 40 and 50% coverage, optimal: 68% (95% UI: 60–70) vs. pro-rata: 22% (95% UI:17–25)), Fig. 3D.

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. Here, we assumed R_eff = 1.1.

Figure 2:

A–C: Optimal, pro-rata, and high-risk allocation strategies with 20% coverage. Optimal allocation strategy to minimize deaths (light and dark blue), high-risk (pink) and pro-rata (green) allocation strategies assuming enough vaccine to cover 20% of the population with a single dose (10% with two doses). Within each panel, the bars represent the percentage vaccinated in each vaccination group. D–E: Prevalence of symptomatic infections. Prevalence of active 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 20% of the population with a single dose (10% 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. Here, we assumed R_eff = 1.1.

Figure 3: Percentage of deaths averted for different levels of SARS-CoV-2 transmission.

Percentage of deaths averted for the optimal allocation strategy to minimize deaths (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 = 1.1 (A-C), 1.3 (D-F), 1.5 (G-I) or 2.4 (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.

For moderate SDE, the optimal vaccine allocation prioritized the high-risk groups (65 and older) with mixed vaccination strategies (one and two doses of vaccine) to increase coverage of these groups when few doses were available, and with two doses of vaccine as coverage increased (Fig. 1B, E, H, K and N), averting up to 18% more deaths than the pro-rata strategy (R_eff = 1.3, 50% coverage, optimal: 71% (95% UI:63–72) vs. pro-rata: 53% (95% UI:45–55)). However, the optimal strategy provided only a modest gain when compared to the high-risk strategy, averting an additional 13% of deaths at low coverage (R_eff = 1.1, 10% coverage, optimal: 43% (95% UI:36–47) vs. high-risk: 30% (95% UI:28–32)) and averted a similar number of deaths for higher levels of coverage (30% or higher), Fig. 3B and E.

In stark contrast, if the vaccine was highly efficacious after one dose, then, for all levels of coverage, the optimal strategy was almost identical to the the pro-rata strategy (Fig. 1C, F, I, L and O), and it averted up to 22% more deaths than the high-risk strategy (R_eff = 1.1, 10% coverage, optimal: 53% (95% UI:45–57) vs. high-risk: 31% (95% UI:28–32)), Fig. 3C and F. While all strategies averted similar number of deaths for high coverage (40 and 50% coverage), the optimal strategy and the pro-rata strategy had the advantage that they significantly slowed down viral transmission and as a result, reduced the overall prevalence of infections (Fig. 4C and F).

Figure 4: Prevalence of active infections (per 100,000) for different levels of background transmission.

Prevalence of 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). Each row represents a different level of SARS-CoV-2 transmission resulting in R_eff = 1.1 (A–C), 1.3 (D–F), 1.5 (G–I) or 2.4 (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.

Results assuming moderate or high background viral transmission.

We next considered that vaccination started under moderate or high background transmission, resulting in an R_eff = 1.5 or R_eff = 2.4, as experienced in WA state early in the pandemic and in November 2020, respectively [25]. Here, the optimal vaccine allocation was always to directly protect those at highest risk (older adults): for low and moderate SDE or for a high SDE combined with high coverage, it was optimal to vaccinate these groups with two doses of vaccine (Fig. 5A, B, D, E, G–O), and if the SDE was high and few doses were available (≤20%) then it was optimal to vaccinate them with a single dose of vaccine (≤20%, Fig. 5C and F) to boost the coverage of that group. If the SDE was low or moderate, the optimal strategy was almost identical to the high-risk strategy , averting up to 47% more deaths than the pro-rata strategy (low SDE, R_eff =1.5, 30% coverage, optimal: 59% (95% UI:48–63) vs. pro-rata:12% (95% UI:11–15)), Fig. 3G, H, J, K). For high SDE, the gain from optimizing vaccine allocation to improve high-risk strategy was relatively small, averting up to 12% more deaths (R_eff = 1.5, 10% coverage optimal: 41% (95% UI:40–42) vs. high-risk: 29% (95% UI:27–29)) but averted up to 23% more deaths than the pro-rata strategy (R_eff = 2.4, 10% coverage, optimal: 36% (95% UI:35–37) vs. pro-rata: 13% (95% UI:12–13) deaths averted). With moderate viral transmission, the optimal strategy to minimize deaths slightly reduced the overall prevalence (regardless of the SDE). However, for high viral transmission, even with enough vaccine to cover 50% of the population, none of the strategies optimized to minimize deaths reduced transmission (Fig. 4G–L).

Figure 5: Optimal vaccine allocation strategies to minimize deaths with different levels of coverage, assuming R_eff =1.5.

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.

Overall, the optimal strategy outperformed the high-risk and the pro-rata strategies the most under low background transmission and low coverage. For all levels of viral transmission considered, regardless of the SDE, 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 = 1.1), 30% coverage (R_eff = 1.3, 1.5) or even 20% coverage (R_eff = 2.4), Fig. 3).

Different metrics have different optimal allocation strategies.

The other metrics we considered capture different disease and healthcare burden impacts of the pandemic, and minimizing each produced a different optimal allocation strategy.

When minimizing outcomes affecting transmission (total infections or total symptomatic infections) and low SDE, the optimal strategy allocated a mix of one and two doses across all age groups, Figs. 6 and S4A and D. In contrast, with moderate or high SDE, the optimal strategy allocated most the available vaccine to the most active group (adults aged 20–49) with a single dose, Figs. 6 and S4B, C, E and F).

Figure 6: 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. Here, we assumed R_eff = 1.1.

When minimizing peak non-ICU hospitalizations and for low or moderate SDE, the optimal strategy prioritized adults aged 65–74 with mixed vaccination strategies to boost coverage of this age group (Figs. 6 and S4G,H). When minimizing ICU hospitalizations with a vaccine with low or moderate SDE, it was optimal to vaccinate the high-risk group (75 and older) at high coverage with two doses of vaccine, and all the other groups with mixed allocations of one and two doses, Figs. 6 and S4J and K. If a single-dose vaccine was highly efficacious, then for all metrics minimizing severe disease (hospitalizations) or deaths and for nearly all levels of coverage, the optimal strategy was in fact the pro-rata strategy , (Figs. 6 and S4I, L and O). However, we noted that even in those scenarios where the optimal and the pro-rata strategies did not coincide, they averted the same number of deaths.

Interestingly, at this level of viral transmission (R_eff = 1.1), the peak hospitalizations (even in absence of vaccine) stayed below WA state desired thresholds (a maximum of 10% of general hospital beds occupied by COVID-19 patients and no overflow of the ICU beds). If viral transmission increased so that R_eff = 1.3, baseline hospitalizations were above the desired thresholds, and only the optimal strategy achieved Washington state goals of staying below these thresholds with as little as 20% vaccination coverage, irrespective of the SDE. For higher coverage, all strategies considered achieved this goal provided that the SDE was moderate or high (Figs. 7 and S5). However, once R_eff ≥ 1.5, the peak non-ICU and ICU hospitalizations for all strategies were higher than desired, even at 50% coverage (Fig. S6).

Figure 7: Prevalence of non-ICU hospitalizations with R_eff =1.3.

Prevalence of non-ICU hospitalizations in absence of vaccine (black), with the optimal allocation strategy to minimize non-ICU hospitalizations (blue), the high-risk strategy (pink) or the pro-rata strategy (green). The gray dashed line indicates 10% occupancy of non-ICU beds in WA state. Each row corresponds to a different vaccination coverage, ranging from 10% (A–C) to 50% (M–O) coverage 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.

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 exclusively 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. 8A–C), irrespective of the SDE. If the reduction in disease was mediated by both a reduction in symptoms, or predominately by preventing infection (VE_SUS), then for low SDE it was still optimal to protect higher-risk groups with two doses (Fig. 8D and G). For moderate SDE, directly protecting the higher-risk groups was still optimal, with two doses if the vaccine was mediated by both effects (moderate VE_SYMP and moderate VE_SUS) and with a single dose if it was exclusively mediated by preventing infection (Fig. 8E and H) However, if the SDE was high, the pro-rata strategy performed best (Fig. 8F and I).

Figure 8: 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. Here, we assumed R_eff = 1.1.

A vaccine preventing only symptomatic disease has the potential to prevent only up to 67% (95% UI: 63–69) of deaths over 6 months compared to 78% (95% UI:72–80) reduction in mortality if exclusively mediated by preventing infection (Fig. 9C and I).

Figure 9: Percentage of deaths averted for different vaccine profiles.

Percentage of deaths averted for the optimal allocation strategy to minimize deaths (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 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. Shaded areas represent results of 1,000 parameter simulations with the top and bottom 2.5% removed. Here, we assumed R_eff = 1.1.

The vaccine efficacy profile had little effect on the cumulative deaths averted by the high-risk strategy (regardless of the SDE) but had a major effect on the pro-rata strategy: while this allocation performed very poorly if the vaccine was exclusively mediated by VE_SYMP and low SDE, with 17% (95% UI:15–19)deaths averted (compared with no vaccination) at 50% coverage, it was much more effective if the vaccine was mediated exclusively by VE_SUS and had a high SDE, averting 78% (95% UI:72–80) of the deaths for the same coverage (Fig. 9A 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. S7). A vaccine acting exclusively by reducing symptoms had a smaller impact on the overall transmission with a maximum of 41% (95% UI:31–48) cumulative infections averted (high SDE, 50% coverage), Fig. S7C) while a vaccine that reduced SARS-CoV-2 acquisition could, if optimally allocated, averted a maximum of 88% (95% UI:83–90) of cumulative infections (high SDE, 50% coverage), Fig. S7I.

Sensitivity analysis

Results assuming asymptomatic infections are 30% as infectious as symptomatic ones:

Due to the wide range of estimates of the relative infectiousness of asymptomatic infections to symptomatic ones (ranging from 0.2 to 1 [35]), we repeated our analysis assuming asymptomatic infections were 30% as infectious as symptomatic ones. The most noticeable differences were found when we analyzed the effect of different vaccine profiles. For low SDE, it was still optimal to directly protect high-risk groups, with two doses if the vaccine was mediated by reducing symptoms or if it was mediated by a combination of reducing symptoms and preventing infection, and with a single dose if it was mediated exclusively by preventing infection (Fig. S8A, D, G). For moderate SDE, mixed allocations were optimal, with more use of single dose vaccination with a vaccine exclusively mediated by preventing infection (Fig. S8B, E, H). For high SDE, regardless of the vaccine profile, the pro-rata strategy was in fact, the optimal strategy (Fig. S8C, F, I). As expected, if asymptomatic infections are considerably less infectious then a vaccine mediated exclusively by reducing symptomatic disease has a higher impact on the overall transmission, preventing as much as 81% (95% UI:76–83) of total infections (compared to a maximum of 41% (95% UI:31–48) total infections averted in the main scenario, Figs. S7C) and S9C.

Results assuming 10% pre-existing immunity at the start of vaccination:

We repeated the main analysis assuming 10% of the population has pre-existing immunity at beginning of vaccination. The results were very similar to those presented in the main scenario, with optimal vaccination strategies favoring single-dose campaigns if the SDE is high (Fig. S10). In this scenario, the epidemic grows faster than in the main scenario and the assumed reduction in contacts presented in Table S2 resulted in R_eff =1.3. As a result, the projected impacts of different strategies are very similar to the ones presented above with R_eff =1.3 with the high-risk strategy being optimal for low and moderate SDE when combined with high coverage and pro-rata strategy being optimal for high SDE irrespective of coverage (Fig. 3D–F).

Results assuming lower or higher infection prevalence at the beginning of vaccination:

We investigated the effect of infection prevalence (number of current SARS-CoV-2 active infections) at the beginning of vaccination in the optimal allocation strategies by considering 0.05 and 0.3% prevalence at the start of vaccination rollout. The optimal strategies were very similar irrespective of initial prevalence (Fig. S11). Choosing the optimal strategy mattered most if vaccination started with lower prevalence: for example, with high SDE and 10% coverage, with 0.05% prevalence, the optimal strategy averted up to 26% more deaths than the high-risk strategy (optimal: 57% (95% UI:47–64) vs high-risk: 31% (95% UI:29–33)), but it only averted a maximum of 14% more deaths (optimal: 44% (95% UI:41–44) vs high-risk: 30% (95% UI:27–30)) if vaccination started with 0.3% prevalence. (Fig. S12C and I).

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 over the time span of six months. For low or high SDE, the optimal strategy was nearly identical to the one described in the main scenario. For moderate SDE, the optimal strategy prioritized the high-risk groups with two doses of vaccine (Fig. S13). With enough vaccine to cover 50% of the population and administering 300K doses per week the optimal strategy averted ~12% more deaths compared to one distributing 150K doses per week. For example, with high SDE and 50% coverage, 87% (95% UI:82–90) and 74% (95% UI:68–77) of deaths were averted compared with no vaccination, vaccinating at 300K and 150K doses per week respectively, Figs. S14C and 3C). Furthermore, at this rate and coverage, the optimal strategy to minimize deaths significantly mitigated transmission irrespective of the SDE, and temporary herd immunity was achieved if the vaccine had a high SDE (Fig. S14G–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 reduced 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 was in fact the pro-rata strategy at low coverage (≤30%), and mixed vaccination strategies that included full coverage of the older adults with a one and two doses of vaccine (Fig S15) for higher coverage. All vaccination strategies averted slightly more deaths due to additional vaccine effects on infectiousness; this was more important at low coverage. With 10% coverage, the optimal strategies averted a maximum of 12% more deaths compared to the main scenario, regardless of the SDE (49% (95% UI:41–54), 56% (95% UI:47–61) and 66% (95% UI:56–71)% deaths averted for low, moderate and high SDE in this scenario versus 42% (95% UI:35–45), 43% (95% UI:36–47) and 53% (95% UI:45–57) deaths averted for the main scenario, Figs. 3 and S16, panels A–C. To note, the gains by using the optimal strategy were more evident in this scenario. For example, with low viral transmission (R_eff = 1.3), high SDE and 10% vaccination coverage, the optimal strategy averted up to 37% more deaths than the high-risk strategy (optimal: 68% (95% UI:55–70) vs. high-risk: 31% (95% UI:29–32) deaths averted) while the optimal strategy averted a maximum of 16% more deaths than the high-risk strategy in the main scenario), Figs. 3F and S16F.

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 doses will need to be prioritized. The current strategies of most countries consider vaccination with full dosage (two doses), but some have proposed vaccinating twice as many people with a single dose and delaying the second dose [36]. An intense debate about how best to use the available vaccine is ongoing [15, 37, 38]. 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 [17]. 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 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 [39, 40, 41] has reached similar conclusions. Furthermore, these results show that vaccinating with a single dose at a faster rate could result in temporary herd immunity, in agreement with previous work [42]. Importantly, as more vaccine becomes available, additional vaccination campaigns may be used to cover everyone with the full two doses of vaccine to provide full protection. In contrast, however, when SARS-CoV-2 transmission is moderate or high (R_eff =1.7 or 3 in our model), we find that 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 allocates vaccine to both the high-risk and the high-transmission groups, consistent with previous work [43]. In contrast, if the level of transmission is moderate or high, it is optimal to directly protect those at high risk of severe disease and death, also in agreement with previous results [44, 20]. Our results highlight the absolute necessity of maintaining social distancing throughout vaccination [45, 46, 47]: 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 has been reported for vaccines requiring two doses, the two licensed in the US (Pfizer and Moderna) and for two others (Sputnik V and AstraZeneca), 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 that 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 that 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 [47], we found that a vaccine that only prevents disease upon infection will have limited population impact, whereas a vaccine preventing infection will have a larger effect in reducing 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) [15], reduced reactogenicity following the first versus the second dose of the mRNA vaccines [18, 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 some of the 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 [48]. We assumed that naturally and vaccine-induced immunity will be at least six months, but the duration of immunity is not yet known; durable immune responses to the Moderna mRNA-1273 vaccine have been found through 3 months post-second-dose [49]. 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, limited data emerging suggests that previous infections might ‘prime’ the immune response, with only one dose boosting immunity [50]. This would be an important consideration for future work when evaluating vaccine allocation over longer time spans with waning immunity. We use age-stratified hospitalization rates based on data from Wuhan, China [51] and mortality rates based on data from France [52]. 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, other factors, such as occupation, have been linked to increased risk of acquisition and severe disease [53, 54]. 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 [55].

Further, deterministic models can overestimate infection dynamics. While comparisons with and without vaccination strategies would not be affected by this, it is possible that our peak hospitalizations are overestimated. Social distancing interventions are being constantly changed and adapted to new challenges when transmission is high, but we kept our social distancing interventions fixed for the duration of the simulations. We included children as possible recipients of vaccine in our analysis, but vaccines are not currently licensed for individuals under 16 years old. However, vaccine trials for younger children are underway for the AstraZeneca and Pfizer vaccines [56] and other vaccine studies in children are being planned, so it is possible that one or more COVID-19 vaccines will be licensed in children within the next 6 months. Importantly, in our model contact rates of children were greatly reduced (by 90% in the contact rates of children at school) and, while the algorithm can in principle select strategies vaccinating children, it seldom does so. In order to run the optimization, we considered a fixed prioritization scheme to model vaccination campaigns, starting always by vaccinating the oldest age-groups. We chose this particular implementation because it most closely mimics current vaccine campaigns around the world and it would favor minimizing deaths, but it is important to note that this prioritization scheme would favor the high-risk strategy and would undermine the pro-rata strategy . In that sense, our results regarding the pro-rata strategy are conservative. Moreover, we used the same implementation for all the disease metrics considered, but other implementations would be more appropriate for different disease metrics. Finally, we have determined optimal allocation strategies in the context of considerable uncertainty as to COVID-19 vaccine profiles and vaccine rollout; once vaccine 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 first identified in the UK, South Africa, and Brazil that are spreading rapidly and circulating in several parts of the globe. It is still unknown how efficacious currently available vaccines will be against each of these variants, with some vaccines exhibiting a decreased efficacy against some of them [57, 58, 29, 59, 60]. Our results show that if the goal is to minimize transmission as a way to minimize the spread of these new variants, then it is optimal to vaccinate the high-transmission groups with one or two doses depending on the SDE. However, 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 [61].

While emerging data suggest that a single dose of the three COVID-19 vaccines (that require two doses) with regulatory licensure or approval in the US and UK might confer high efficacy [2, 62, 63], the duration of protection remains 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 [64]. If single-dose immunity lasts for at least 6 months, our results show that if viral transmission is low, 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.