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.

中文翻译：

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关于图上流行病学模型的连续极限：收敛和近似结果

我们专注于在图上定义的流行病学模型（典型的 SIR 系统），并研究随着图中顶点数量的变化解的渐近行为。通过依赖图子理论，我们提供了极限的表征并建立了收敛结果。我们还提供确定性和随机离散化的近似结果。