We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.
de Dios, B., Dovetta, S., Spinolo, L. (2024). On the continuum limit of epidemiological models on graphs: convergence and approximation results. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 34(8), 1483-1532 [10.1142/s0218202524500271].
On the continuum limit of epidemiological models on graphs: convergence and approximation results
de Dios, Blanca Ayuso;
2024
Abstract
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.
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de Dios-2024-Math Mod Meth Appl Sci-AAM.pdf
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