Multi-scale local network structure critically impacts epidemic spread and interventions

Omar Eldaghar, Michael W Mahoney and David F Gleich

PLOS Complex Systems, 2026, vol. 3, issue 9, 1-28

Abstract: Network epidemic simulation enables fine-grained understanding of epidemic behavior. However, empirical samples of interaction networks display properties that are challenging to capture with popular synthetic models of networks. Our empirical results show that epidemic spread behavior is sensitive to a form of multi-scale local structure that is absent in common baseline models, (e.g., Erdős–Rényi, Chung-Lu, etc). This structure critically impacts the effect of local quarantining and stops epidemic spread in samples of interaction networks, even when it cannot be halted in simple synthetic models of those networks. Insights from our analysis include how epidemics on networks with widespread multi-scale local structure are easier to mitigate, as well as characterizing which nodes are ultimately not likely to be infected. We demonstrate that this structure results from more than just local triangle structure in the network, and we illustrate processes based on homophily or social influence and random walks that suggest how this multi-scale local structure arises and use it to cleanly isolate intervention sensitivity to multi-scale local structure.Author summary: Epidemic spread is strongly dependent on the patterns and structures inherent in human contact networks. Contact patterns give rise to structural network features that can impact epidemic spread and control in complex ways. A subtle but prominent feature of real-world networks is rich multi-scale structure that manifests as groups of well-connected nodes at multiple size scales. We study this multi-scale structure and show that it can have a large impact on the control of epidemics in real networks. This structure also provides insight on what portions of the network are more resilient to infection while proving more reliable than traditional metrics such as average degree or the dominant eigenvalue. We also give generative models that reliably reproduce this structure as well as distinguish this structure from the closing of triangles and cleanly isolate the impact of this structure on epidemic spreading.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcsy00:0000116

DOI: 10.1371/journal.pcsy.0000116

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