When allocating limited vaccines to control an infectious disease, policy makers frequently have goals relating to individual health benefits (e.g., reduced morbidity and mortality) as well as population-level health benefits (e.g., reduced transmission and possible disease eradication). We consider the optimal allocation of a limited supply of a preventive vaccine to control an infectious disease, and four different allocation objectives: minimize new infections, deaths, life years lost, or quality-adjusted life years (QALYs) lost due to death. We consider an SIR model with $n$ interacting populations, and a single allocation of vaccine at time 0. We approximate the model dynamics to develop simple analytical conditions characterizing the optimal vaccine allocation for each objective. We instantiate the model for an epidemic similar to COVID-19 and consider $n=2$ population groups: one group (individuals under age 65) with high transmission but low mortality and the other group (individuals age 65 or older) with low transmission but high mortality. We find that it is optimal to vaccinate younger individuals to minimize new infections, whereas it is optimal to vaccinate older individuals to minimize deaths, life years lost, or QALYs lost due to death. Numerical simulations show that the allocations resulting from our conditions match those found using much more computationally expensive algorithms such as exhaustive search. Sensitivity analysis on key parameters indicates that the optimal allocation is robust to changes in parameter values. The simple conditions we develop provide a useful means of informing vaccine allocation decisions for communicable diseases.

在分配有限的疫苗来控制传染病时，政策制定者的目标通常与个人健康益处（例如，降低发病率和死亡率）以及人口水平的健康益处（例如，减少传播和可能的疾病根除）相关。我们考虑了有限供应的预防性疫苗的最佳分配以控制传染病，以及四个不同的分配目标：最大限度地减少新感染、死亡、损失的生命年或因死亡而损失的质量调整生命年 (QALY)。我们考虑一个 SIR 模型$n$相互作用的人群，以及在时间 0 时的单一疫苗分配。我们近似模型动力学以开发简单的分析条件，以表征每个目标的最佳疫苗分配。我们为类似于 COVID-19 的流行病实例化模型并考虑$n=\mathrm{2个}$人口群体：一组（65 岁以下的人）传播率高但死亡率低，另一组（65 岁或以上的人）传播率低但死亡率高。我们发现，为年轻人接种疫苗以最大限度地减少新感染是最佳的，而为老年人接种疫苗以最大程度地减少死亡、生命年损失或因死亡导致的 QALY 损失是最佳的。数值模拟表明，根据我们的条件得出的分配与使用计算成本更高的算法（例如穷举搜索）找到的分配相匹配。对关键参数的敏感性分析表明，最优分配对参数值的变化具有鲁棒性。我们开发的简单条件提供了一种有用的方法，可以为传染病的疫苗分配决策提供信息。