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

Blanca Ayuso de Dios, Simone Dovetta, Laura V. Spinolo

Published 2022-11-03Version 1

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. We illustrate the analytic findings through an extensive set of numerical simulations.