A highly effective method for controlling the spread of an infectious disease is vaccination. However, there are many situations where vaccines are in limited supply. The ability to determine, under this constraint, a vaccination strategy which minimises the number of people that become infected over the course of a potential epidemic is essential. Two questions naturally arise: when is it best to allocate vaccines, and to whom should they be allocated? We address these questions in the context of metapopulation models of disease spread. We discover that it is optimal to distribute all vaccines prophylactically, rather than withholding until infection is introduced. For small metapopulations, we provide a method for determining the optimal allocation. As the optimal strategy becomes computationally intensive to obtain when the population size increases, we detail an approximation method to determine an approximately optimal vaccination scheme. Through comparisons with other strategies in the literature, we find that our approximate strategy is superior.
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