To minimize deaths, the optimal policy is for the first two batches of vaccine to be allocated to high-risk people, followed by schoolchildren (ages 5–17) and then young adults (ages 18–44) (Figure 1A). To minimize hospitalizations, the first five batches should be allocated to schoolchildren and young adults, with a small amount of vaccine also allocated to high-risk people in the fifth batch (Figure 1B).
Figure 1. Optimal vaccine allocation for different vaccine delivery schedules, different values of , and different objectives. The delivery schedule "45M + 4 × 20M doses" corresponds to five batches of vaccine delivery: 45M doses on (more ...)
As the basic reproductive number (
) increases, optimal allocation to minimize deaths no longer includes schoolchildren (Figure 1C), while optimal allocation for hospitalizations shifts to include high-risk people (Figure 1D). This is due in part to acquired immunity: for
, only 11% of schoolchildren have been infected before the first vaccine is available on 15 October, whereas, for
, 45% of schoolchildren have been infected by 15 October.
The optimal allocation is sensitive to the scheduling of release times. Consequently, evaluation of each batch separately does not generate the allocation strategy that is optimal overall (see Text S1 and Figures S3–S10). For example, when only two total batches are available (45 million doses on 15 October and 20 million on 22 October), deaths can be minimized by allocating the first batch to schoolchildren and the second batch to adults aged 18–44 (Figure S3). In contrast, when 3 total batches are available (45 million doses on 15 October and 20 million on each of 22 October and 29 October), the first two batches are optimally split between schoolchildren and high-risk people and the third batch is used exclusively on high-risk people.
The projected reductions in infections, deaths, and hospitalizations are substantial for both sets of optimized vaccination strategies (Figure 2). The strategy that minimizes hospitalizations is predicted to reduce the total attack rate more effectively than the strategy that minimizes deaths (11.4% versus 15.2% of the population infected, respectively). Comparing the number of deaths and hospitalizations, the strategy that minimizes deaths results in 8000 fewer deaths (a 23% reduction) and 44,000 more hospitalizations (a 9% increase) than the strategy that minimizes hospitalizations. Since the strategy that minimizes deaths also greatly reduces hospitalizations, it may be preferred by decision makers.
Figure 2. The impact on infections, deaths, and hospitalizations for different vaccine delivery schedules and different objectives, with .
The staggered vaccine delivery schedule that we considered had a total of 125 million doses in five batches starting on 15 October. To explore the effect of the delay in vaccine delivery, we also calculated the optimal allocations when all 125 million doses were delivered in one batch, either on 15 October or before the outbreak began (Figure 1). The epidemiological impact of the initial vaccination delay is substantial: the staggered release results in 23% more deaths and 26% more hospitalizations, respectively, compared to optimal allocation of the complete distribution in October. By contrast, the optimal distribution of 125 million doses before the outbreak begins prevented the outbreak entirely (Figure 2).