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

TL;DR

This paper investigates the asymptotic behavior of SIR epidemiological models on large graphs, establishing convergence to a graphon-based limit and providing approximation results for different discretizations.

Contribution

It introduces a framework using graphons to analyze the continuum limit of epidemic models on graphs, with new convergence and approximation results.

Findings

Convergence of epidemic solutions to a graphon limit as graph size increases

Approximation methods for deterministic and random graph discretizations

Characterization of the continuum limit for large-scale epidemiological models

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 so called graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.