Year: 2025
Type: article
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.
Source: Journal of Mathematical Biology
Author: Carlos Segovia
Institution: Universidad Nacional Autónoma de México
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4414247335