Epidemic threshold in pairwise models for clustered networks: closures and fast correlations

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• The epidemic threshold is a key metric in epidemic modeling on networks.
• Existing models struggle with clustered networks, lacking theoretical results for pairwise models.
• Analytical solutions for epidemic thresholds in complex network structures are limited.

Purpose of the Study:

• To derive an analytical expression for the epidemic threshold in clustered networks using pairwise models.
• To validate the derived analytical threshold against numerical solutions of the full system.
• To investigate the influence of network properties and model choices on the epidemic threshold.

Main Methods:

• Application of perturbation theory and exploitation of fast variables within pairwise models.
• Derivation of an analytical formula for the epidemic threshold.
• Numerical simulations of epidemic dynamics on clustered networks for validation.

Main Results:

• An analytical epidemic threshold was successfully derived for pairwise models on clustered networks.
• The derived threshold shows excellent agreement with numerical solutions across various network parameters.
• The analytical threshold's form is sensitive to the choice of closure, emphasizing model selection importance.

Conclusions:

• The developed perturbation theory method provides an accurate analytical epidemic threshold for clustered networks.
• This method advances the understanding of epidemic dynamics in complex, real-world network structures.
• The approach is potentially extensible to other systems exhibiting fast variables.