ArticleJournal of mathematical biology2025
Petri nets in epidemiology.
Article in Journal of mathematical biology, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- Dual-Model framework for CHIKV transmission modeling: ODE and Petri Net Analysis of the 2025 Foshan outbreak.BMC public health · 2026Article
- A Numerical Comparison of Petri Net and Ordinary Differential Equation SIR Component Models.IEEE access : practical innovations, open solutions · 2026Article
- Article
- The Basic Reproduction Number for Petri Net Models: A Next-Generation Matrix Approach.Applied sciences (Basel, Switzerland) · 2025Article
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1 author.
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Abstract
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe that any epidemiological model has the basic structures found in the SIR model of Kermack-McKendrick. This means that the basic reproduction number depends only on three substructures inside the Petri net, which are also given by three Petri nets inside, representing the susceptible population, the infection process, and the infected population. The five assumptions of the next-generation matrix method given by van den Driessche-Watmough can be described geometrically using Petri nets. Thus, the next-generation matrix results in a matrix of flows between the infection compartments with a dominant eigenvalue given by the basic reproduction number.
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