论文标题
最佳疫苗接种：Cordons Sanitaires，还原的人群和最佳射线
Optimal vaccinations: Cordons sanitaires, reducible population and optimal rays
论文作者
论文摘要
我们考虑将（完美）疫苗剂量分配给无限维型的双向目标问题，以便同时最大程度地减少疫苗接种成本和有效的繁殖数量$ r_e $，该数字定义为有效下一代操作员的光谱半径。 在这个一般框架中，我们证明了警戒线疗养院，即有效地脱离非疫苗接种人群的策略，可能不是最佳的，但仍然比“最坏的”疫苗接种策略要好。受图理论的启发，我们还计算了最低的成本，该成本可确保使用独立集中没有感染。将整个人群的Frobenius分解为不可约合的子人群，我们为最佳（“最佳”和“最坏”）疫苗接种策略提供了一些明确的公式。最终，我们为最佳策略的缩放提供了一些足够的条件，以保持最佳状态。
We consider the bi-objective problem of allocating doses of a (perfect) vaccine to an infinite-dimensional metapopulation in order to minimize simultaneously the vaccination cost and the effective reproduction number $R_e$, which is defined as the spectral radius of the effective next-generation operator. In this general framework, we prove that a cordon sanitaire, that is, a strategy that effectively disconnects the non-vaccinated population, might not be optimal, but it is still better than the "worst" vaccination strategies. Inspired by graph theory, we also compute the minimal cost which ensures that no infection occurs using independent sets. Using Frobenius decomposition of the whole population into irreducible sub-populations, we give some explicit formulae for optimal ("best" and "worst") vaccinations strategies. Eventually, we provide some sufficient conditions for a scaling of an optimal strategy to still be optimal.
