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Dimension reduction in higher-order contagious phenomena.

Subrata Ghosh1, Pitambar Khanra2, Prosenjit Kundu3

  • 1Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India.

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Summary
This summary is machine-generated.

We developed a simplified model to understand epidemic spreading in complex networks. Higher-order interactions impact disease spread and network resilience, leading to abrupt transitions in population health.

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Area of Science:

  • Network Science
  • Epidemiology
  • Mathematical Modeling

Background:

  • Epidemic spreading models are crucial for understanding disease dynamics in populations.
  • Heterogeneous networks and higher-order interactions significantly influence epidemic behavior.
  • Existing models often struggle to capture the complexity of real-world network structures.

Purpose of the Study:

  • To develop a reduced-order model for epidemic dynamics on heterogeneous networks with higher-order interactions.
  • To analyze the impact of network topology and higher-order interactions on epidemic spreading.
  • To quantify network resilience against disease propagation.

Main Methods:

  • Developed a one-dimensional resilience function to reduce the dimensionality of the susceptible-infected-susceptible (SIS) model.
  • Employed analytical techniques to derive microscopic and macroscopic behaviors of the system.
  • Utilized spectral analysis for an alternative dimension reduction framework to identify disease onset.

Main Results:

  • Microscopic state (healthy individuals per node) inversely scales with node degree and is diminished by higher-order interactions.
  • Macroscopic system state (infectious/healthy population fraction) exhibits abrupt transitions due to higher-order interactions.
  • Network resilience quantification reveals sensitivity to topological changes affecting stable infected populations.

Conclusions:

  • The developed reduction methods accurately capture epidemic spreading behavior in complex networks.
  • Higher-order interactions introduce abrupt transitions and alter network resilience.
  • The framework is extendable to various dynamical models on networks.