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On the continuum limit of epidemiological models on graphs: Convergence and approximation results

Università degli Studi Milano–Bicocca, Dipartimento di Matematica e Applicazioni, via Roberto Cozzi 55, 20126 Milano, Italy

CNR-IMATI “E. Magenes”, via Ferrata 5, 27100 Pavia, Italy

E-mail Address: [email protected]

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Simone Dovetta

Politecnico di Torino, Dipartimento di Scienze Matematiche, Corso Duca degli Abruzzi 24, 10125 Torino, Italy

E-mail Address: [email protected]

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, and

Laura V. Spinolo

https://orcid.org/0000-0002-7696-8873

CNR-IMATI “E. Magenes”, via Ferrata 5, 27100 Pavia, Italy

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0218202524500271Cited by:0 (Source: Crossref)

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.

Communicated by N. Bellomo

Keywords:

AMSC: 35Q92, 92D30, 35R02, 05C99

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