Related Experiment Video
Updated: Aug 6, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
A Graph-Theoretical Framework for Automated Computation of Reproduction Numbers in Deterministic Epidemiological
Alexandre Simard1, Jacques Bélair2,3,4
1Département de mathématiques et de statistique, Université de Montréal, C.P. 6128 succursale Centre-ville, H3C 3J7, Montréal, QC, Canada. as.simard99@gmail.com.
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 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.
Related Concept Videos
Modeling with Differential Equations
Statistical Methods for Analyzing Epidemiological Data
Steps in Outbreak Investigation
Exponential Equations for Modeling Growth
Population Growth
Statistical Software for Data Analysis and Clinical Trials
