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.
Timing is of crucial importance for successful vaccination. To avoid a large outbreak, vaccines are administered preferably as quickly as possible. However, in the early stages of an outbreak the information on the disease is limited and waiting with the intervention allows to design a more tailored vaccination strategy. In this paper we study the resulting tradeoff between timing of vaccination and the effectiveness of the response.We model disease progression using the seminal SIR model, and consider a decision maker who allocates her budget over two vaccine types: an early aspecific vaccine and a later specific vaccine. We analytically characterize the switching curve separating the parameter space region where the late specific vaccine is preferred from the region where the early aspecific type is preferred. More importantly, weshow that the decision maker should not only consider pure strategies, i.e., strategies which spend the entire budget on one of the types. Instead, she should suitably invest in both vaccine types to benefit both from the early response and from the good vaccine. We prove that at the switching curve, such a hybrid strategy is strictly better than either of the pure strategies due to the non-linear dynamics of epidemics. Numerical experiments show that the associated benefit of hybrid strategies over pure strategies in terms of reduction of the number of infections may be more than 50%. Such experiments also substantiate our restriction to two vaccine types.
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