Universality classes in the time evolution of epidemic outbreaks on complex networks

Area of Science:

• Epidemiology
• Network Science
• Computational Biology

Background:

• Understanding epidemic dynamics is crucial for public health interventions.
• Disease transmission models, like the susceptible-infected (SI) model, are essential for predicting outbreak trajectories.
• Network structure significantly influences disease spread patterns.

Purpose of the Study:

• To investigate the full temporal evolution of epidemic outbreaks in complex networks using the SI model.
• To identify universal patterns of epidemic growth determined by network topology.
• To develop analytical formulas for epidemic prevalence and scaling relations.

Main Methods:

• Theoretical analysis of epidemic spread.
• Large-scale numerical simulations on various network structures.
• Application of the susceptible-infected (SI) model.

Main Results:

• Two universal epidemic growth patterns were identified: Gompertz-like curves in small-world networks and Avrami-type dynamics in fractal networks.
• These patterns define distinct universality classes, robust across different transmission rates.
• Explicit analytical formulas for epidemic prevalence and scaling relations were derived.

Conclusions:

• Network structure dictates epidemic growth dynamics, leading to distinct universality classes.
• Early exponential growth is characteristic only of small-world networks, not fractal networks.
• This study provides a unified framework for understanding epidemic dynamics across diverse network topologies.