The effective reproduction number: convexity, concavity and invariance
| Autor: | Delmas, Jean-François, Dronnier, Dylan, Zitt, Pierre-André |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $R_e(\eta)$ of the matrix product $\mathrm{Diag}(\eta)K$, as a function of $\eta\in\mathbb{R}_+^n$. The matrix $K$ and the vector $\eta$ 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 $\eta$. 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. Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:2110.12693 |
| Databáze: | arXiv |
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