Percolation on heterogeneous networks as a model for epidemics

Area of Science:

• Epidemiology
• Mathematical Modeling
• Statistical Physics

Background:

• Standard epidemiological models often assume uniform susceptibility to infection.
• Real-world disease spread can be influenced by variations in individual susceptibility.
• Understanding heterogeneity is crucial for accurate epidemic prediction.

Purpose of the Study:

• To investigate the impact of varying susceptibility on disease spread using a spatial bond percolation model.
• To analyze how heterogeneity affects epidemic outbreak criteria and spatial patterns.
• To explore these effects on small-world lattices.

Main Methods:

• Development of a spatial bond percolation model incorporating random bond strengths to represent varying susceptibility.
• Analysis of lattice structures, including standard lattices and small-world lattices.
• Simulation and theoretical analysis of epidemic spread patterns and outbreak thresholds.

Main Results:

• Strong heterogeneity in susceptibility leads to highly patchy epidemic spread.
• The criterion for epidemic outbreak is significantly dependent on the degree of heterogeneity.
• These effects are amplified on small-world lattices compared to standard lattices.

Conclusions:

• Heterogeneity in susceptibility is a critical factor in disease dynamics, leading to non-uniform spread.
• The findings challenge standard epidemiological models and highlight the importance of incorporating real-world variations.
• Heterogeneity may influence the phylogenetic distance distribution of pathogens.