The Basic Reproduction Number for Bounded Linear Operators on Ordered Banach Spaces
Functional Analysis
2026-02-12 v1 Dynamical Systems
Abstract
A basic reproduction number, , 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 and . Here we extend these results to more general cone-preserving bounded linear operators acting on Banach spaces.
Cite
@article{arxiv.2602.10358,
title = {The Basic Reproduction Number for Bounded Linear Operators on Ordered Banach Spaces},
author = {Zachary Gregg and Patrick De Leenheer},
journal= {arXiv preprint arXiv:2602.10358},
year = {2026}
}