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arXiv · 2602.10358

The Basic Reproduction Number for Bounded Linear Operators on Ordered Banach Spaces

Zachary Gregg·Patrick De Leenheer
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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.

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Zachary Gregg, Patrick De Leenheer. 2026-02-10. The Basic Reproduction Number for Bounded Linear Operators on Ordered Banach Spaces. https://arxiv.org/abs/2602.10358

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