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Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

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Area of Science:

  • Network Science
  • Mathematical Epidemiology
  • Computational Biology

Background:

  • Network clustering, the tendency for connected nodes to form triangles, is common but difficult to model.
  • Existing models often rely on fully connected subgraphs, limiting analysis of complex network structures.
  • Epidemic modeling on networks with non-fully connected subgraphs remains a significant challenge.

Purpose of the Study:

  • To develop a general and automated approach for deriving mean-field models of epidemic dynamics.
  • To provide precise control over subgraph arrangements and network characteristics (degree, variance, clustering).
  • To investigate the impact of higher-order network structures on epidemic spread.

Main Methods:

  • Developed a method to derive ordinary differential equations (ODEs) for mean-field models.
  • Enabled automated control over subgraph composition and network metrics.
  • Generated families of networks with varying subgraph structures but constant classical metrics.

Main Results:

  • The derived mean-field models accurately predict system-level quantities like infection prevalence.
  • Demonstrated the ability to generate networks with controlled higher-order structures (e.g., loops).
  • Showed that different subgraph compositions, even with identical degree distributions and clustering, significantly alter epidemic dynamics.

Conclusions:

  • The new approach offers unprecedented control over network generation for epidemiological modeling.
  • Higher-order network structures, beyond simple degree distribution and clustering, play a crucial role in epidemic dynamics.
  • This framework facilitates a deeper understanding of how network topology influences disease transmission.