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Dose-Optimal Vaccine Allocation over Multiple Populations

机译：多个人群的剂量最佳疫苗分配

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摘要

Vaccination is an effective way to prevent an epidemic. It results in immunity for the vaccinated individuals, but it also reduces the infection pressure for unvaccinated people. Thus people may actually escape infection without being vaccinated: the so-called herd effect. We analytically study the relation between the herd effect and the vaccination fraction for the seminal SIR compartmental model, which consists of a set of differential equations describing the time course of an epidemic. We prove that the herd effect is in general convex-concave in the vaccination fraction and give precise conditions on the epidemic for the convex part to arise. We derive the significant consequences of these structural insights for allocating a limited vaccine stockpile to multiple non-interacting populations. We identify for each population a unique vaccination fraction that is most efficient per dose of vaccine: our dose-optimal coverage. We characterize the solution of the vaccine allocation problem and we show the crucial importance of the dose-optimal coverage. A single dose of vaccine may be a drop in the ocean, but multiple doses together can save a population. To benefit from this, policy makers should select a subset of populations to which the vaccines are allocated. Focusing on a limited number of populations can make a significant difference, whereas allocating equally to all populations would be substantially less effective.
机译：接种疫苗是预防流行病的有效方法。它可以使接种疫苗的人产生免疫力，但也可以降低未接种疫苗的人的感染压力。因此，人们实际上可以在没有接种疫苗的情况下逃脱感染：所谓的牛群效应。我们分析性地研究了牛群SIR隔离模型的畜群效应与疫苗接种率之间的关系，该模型由一组描述流行病时间过程的微分方程组成。我们证明，在疫苗接种率中，羊群效应总体上是凸凹的，并为流行病的精确条件提供了凸形部分出现的条件。我们得出这些结构见解对将有限的疫苗储备分配给多个非相互作用种群的重大影响。我们为每个人群确定一种独特的疫苗接种比例，该疫苗接种比例是每剂疫苗最有效的：我们的剂量最佳覆盖率。我们描述了疫苗分配问题的解决方案，并展示了剂量最优覆盖范围的至关重要性。单剂疫苗可能是沧海一粟，但多剂合起来可以拯救一群人。为了从中受益，政策制定者应选择疫苗要分配给的部分人群。只关注有限数量的人群会产生重大影响，而对所有人群进行均等分配的效果将大大降低。

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