On the continuum limit of epidemiological models on graphs: Convergence and approximation results-Reference-Cited by-同舟云学术

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

Published:2024-04-30 Issue:08 Volume:34 Page:1483-1532
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Ayuso de Dios Blanca¹²^ORCID,Dovetta Simone³,Spinolo Laura V.²^ORCID

Affiliation:

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

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

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

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.

Funder

Nonlinear dispersive equations in presence of singularities

European Union - Next Generation EU within the PRIN 2022 program

Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica

PRIN 2020

PRIN 2022

PRIN 2022 PNRR

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202524500271

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