2022/11/21 by Jean‐François Delmas, Delmas, Jean-François, Dylan Dronnier +3 · 1 citation
Mathematics · Medicine · #COVID-19 epidemiological studies #Mathematical and Theoretical Epidemiology and Ecology Models #Virology and Viral Diseases
paper · pdf · doi:10.48550/arxiv.2211.11862
Motivated by the question of optimal vaccine allocation strategies in heterogeneous population for epidemic models, we study various properties of the effective reproduction number. In the simplest case, given a fixed, non-negative matrix K, this corresponds mathematically to the study of the spectral radius Re(η) of the matrix product Diag(η)K, as a function of η∈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 Re to be convex or a concave. Eventually, we provide equivalence properties on models which ensure that the function Re is unchanged.