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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...

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Related Experiment Video

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

Phase transitions in the quadratic contact process on complex networks.

Chris Varghese¹, Rick Durrett

¹Department of Physics, Duke University, Durham, North Carolina, USA. varghese@phy.duke.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

The quadratic contact process (QCP) on complex networks shows distinct behaviors. Unlike regular graphs, power-law networks exhibit a continuous phase transition for infection spread.

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Area of Science:

Statistical Physics
Network Science
Epidemiology Modeling

Background:

The linear contact process is a fundamental model for epidemic spread.
The quadratic contact process (QCP) extends this by requiring two infected individuals to infect a susceptible one.
Previous QCP studies were limited to regular lattices.

Purpose of the Study:

To extend the quadratic contact process (QCP) to complex network topologies.
To investigate two QCP variants: vertex-centered (VQCP) and edge-centered (EQCP).
To analyze the impact of network structure on QCP dynamics.

Main Methods:

Definition of VQCP and EQCP models with specific birth and death events.
Analysis on random regular, Erdős-Rényi, and power-law random graphs.
Combination of mean-field calculations and computer simulations.

Main Results:

Discontinuous phase transitions and bistability observed on random regular and Erdős-Rényi graphs.
Continuous phase transition found on heavy-tailed power-law graphs.
Critical birth rate is positive for regular/Erdős-Rényi graphs, but zero for power-law graphs.

Conclusions:

Network topology significantly influences the phase transition behavior of the QCP.
Power-law networks exhibit fundamentally different epidemic spread dynamics compared to regular networks.
The QCP provides a richer framework for understanding disease dynamics on diverse network structures.