Vaccination is one of the most effective ways to prevent and/or control the outbreak of infectious diseases. This medical intervention also brings about many logistical questions. In the past years, the Operations Research/Operations Management community has shown a growing interest in the logistical aspects of vaccination. However, publications on vaccine logistics often focus on one specific logistical aspect. A broader framework is needed so that open research questions can be identified more easily and contributions are not overlooked. In this literature review, we combine the priorities of the World Health Organization for creating a flexible and robust vaccine supply chain with an Operations Research/Operations Management supply chain perspective. We propose a classification for the literature on vaccine logistics to structure this relatively new field, and identify promising research directions. We classify the literature into the following four components: (1) product, (2) production, (3) allocation, and (4) distribution. Within the supply chain classification, we analyze the decision problems for existing outbreaks versus sudden outbreaks and developing countries versus developed countries. We identify unique characteristics of the vaccine supply chain: high uncertainty in both supply and demand; misalignment of objectives and decentralized decision making between supplier, public health organization and end customer; complex political decisions concerning allocation and the crucial importance of deciding and acting in time.

V accination 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.

Abstract'Critical vaccination coverages' are vaccination allocations that result in an effective reproduction ratio of one. In a population with interacting subpopulations there are many different critical vaccination coverages. To find the most efficient critical vaccination coverage, we define the following optimization problem: minimize the required amount of vaccines to obtain an effective reproduction ratio of exactly one. We prove that this optimization problem is equivalent to the problem of maximizing the proportion of susceptibles that escape infection during an epidemic (i.e., maximizing the herd effect).We propose an efficient general algorithm to solve these optimization problems based on PerronFrobenius theory. We study two special cases that provide further insight into these optimization problems. First, we derive an explicit analytic solution for the case of two interacting populations. Second, we derive an efficient algorithm for the case of multiple populations that interact according to separable mixing. In this algorithm the subpopulations are ordered by their ratio of population size to reproduction ratio. Allocating vaccines based on this priority order results in an optimal allocation. We apply our solutions in a case study for pre-pandemic vaccination in the initial phase of an influenza pandemic where the entire population is susceptible to the new influenza virus. The results show that for the optimal allocation the critical vaccination coverage is achieved for a much smaller amount of vaccines as compared to allocations proposed previously.

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