Universality classes of the generalized epidemic process on random networks

Area of Science:

• Statistical physics
• Network science
• Epidemiology modeling

Background:

• The generalized epidemic process (GEP) models social contagions with cooperative effects.
• Understanding phase transitions in such models is crucial for predicting contagion dynamics.
• Poisson random networks provide a tractable framework for studying these processes.

Purpose of the Study:

• To analyze the universality classes of the GEP on Poisson random networks.
• To investigate the rich phase transitional behaviors, including continuous and discontinuous transitions and tricriticality.
• To verify field-theoretical results using numerical methods and finite-size scaling theory.

Main Methods:

• Development of a comprehensive finite-size scaling theory.
• Numerical confirmation of static and dynamic scaling behaviors.
• Proposal of a criterion for the discontinuous transition line.

Main Results:

• Static and dynamic scaling behaviors of the GEP near continuous phase transitions and tricriticality were numerically confirmed.
• The proposed criterion for the discontinuous transition line was shown to coincide with the bond percolation threshold.
• The study confirms field-theoretical predictions for GEP universality classes.

Conclusions:

• The GEP on Poisson random networks exhibits complex phase transitions, including continuous, discontinuous, and tricritical points.
• Finite-size scaling theory effectively describes the GEP's behavior near critical points.
• The bond percolation threshold serves as a key indicator for discontinuous transitions in the GEP model.