The Basic Reproduction Number for Bounded Linear Operators on Ordered Banach Spaces
Abstract
A basic reproduction number, $R_0$, is a concept encountered frequently in the study of ecological and epidemiological models. It is routinely used to determine the stability of an extinction or a disease-free fixed point or steady state. It is well-known that for linear models described by non-negative matrices, the spectral radius of the matrix is always contained in an interval with endpoints $1$ and $R_0$. Here we extend these results to more general cone-preserving bounded linear operators acting on Banach spaces.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Differential Equations Analysis
Advanced Banach Space Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint