A Graph-Theoretical Framework for Automated Computation of Reproduction Numbers in Deterministic Epidemiological Models.

Authors

Alexandre Simard, Jacques Bélair

Published in

Bulletin of mathematical biology. Volume 88. Issue 8. Jul 23, 2026. Epub Jul 23, 2026.

Abstract

We introduce a graph-theoretical approach to epidemiological modeling that automates the derivation of the differential equations associated with a model and the computation of its base and real-time reproduction numbers. Our framework defines a novel structure called "epidemiological hypergraphs", graphs extended with epidemiological characteristics in order to automatize their analysis. The main focus of this article is to index a few individuals of interest and explicitly track their secondary infections, emulating the granularity of agent-based models. This structure also removes the need for model-specific analysis, improving reproducibility and enhancing accessibility for epidemiologists. We validate consistency with the next-generation matrix approach for the base reproduction number while demonstrating superior analytical accuracy over the classical estimate $R_t=S/N·R_0$ for the real-time reproduction number, especially in scenarios where parameters evolve in time or when variants are introduced. Our approach offers an adaptive mathematical framework for real-time epidemic tracking and intervention planning.

PMID:
42493751
Bibliographic data and abstract were imported from PubMed on 24 Jul 2026.

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