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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.
Bulletin of Mathematical Biology
|July 23, 2026
Summary
We developed epidemiological hypergraphs, a novel graph theory method for automated epidemic modeling. This approach enhances accuracy in tracking infections and calculating reproduction numbers for better public health planning.
Area of Science:
- Epidemiology
- Graph Theory
- Mathematical Modeling
Background:
- Traditional epidemiological models often require complex, model-specific analyses.
- Calculating real-time reproduction numbers can be challenging, especially with evolving parameters or new variants.
Purpose of the Study:
- To introduce a novel graph-theoretical framework for automated epidemiological analysis.
- To enhance the accuracy and accessibility of epidemiological modeling and real-time tracking.
Main Methods:
- Development of "epidemiological hypergraphs" to represent disease transmission dynamics.
- Automated derivation of differential equations and computation of reproduction numbers (R0 and Rt).
- Tracking secondary infections with agent-based model granularity.
Main Results:
- Validated consistency with the next-generation matrix for the basic reproduction number.
- Demonstrated superior analytical accuracy over classical estimates for the real-time reproduction number.
- Framework offers improved reproducibility and accessibility for epidemiologists.
Conclusions:
- Epidemiological hypergraphs provide an adaptive mathematical framework for real-time epidemic tracking.
- This approach facilitates more accurate intervention planning and disease management.
- The method enhances understanding of transmission dynamics in complex scenarios.
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