论文标题
有效的繁殖编号：凸，凹和不变性
The effective reproduction number: convexity, concavity and invariance
论文作者
论文摘要
我们研究了\ emph {有效繁殖数}的各种特性的异质种群中最佳疫苗分配策略的问题。在最简单的情况下，给定固定的非负矩阵$ k $，这与矩阵product $ \ mathrm {diag}（η）k $的光谱半径$ r_e（η）$的研究相对应矩阵$ k $和向量$η$可以解释为下一代操作员和疫苗接种策略。这可以在无限尺寸的情况下推广，在该情况下，矩阵$ k $被正面的紧凑型操作员取代，该操作员由非负函数$η$组成。 我们为函数$ r_e $提供了足够的条件，即凸面或凹面。最终，我们在模型上提供等价属性，以确保函数$ r_e $没有变化。
Motivated by the question of optimal vaccine allocation strategies in heterogeneous population for epidemic models, we study various properties of the \emph{effective reproduction number}. In the simplest case, given a fixed, non-negative matrix $K$, this corresponds mathematically to the study of the spectral radius $R_e(η)$ of the matrix product $\mathrm{Diag}(η)K$, as a function of $η\in\mathbb{R}_+^n$. The matrix $K$ and the vector $η$ can be interpreted as a next-generation operator and a vaccination strategy. This can be generalized in an infinite dimensional case where the matrix $K$ is replaced by a positive integral compact operator, which is composed with a multiplication by a non-negative function $η$. We give sufficient conditions for the function $R_e$ to be convex or a concave. Eventually, we provide equivalence properties on models which ensure that the function $R_e$ is unchanged.
