Mixed-order phase transition in a two-step contagion model with a single infectious seed
Wonjun Choi1, Deokjae Lee1, B Kahng1
1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
Physical Review. E
|March 17, 2017
Summary
This study explores a novel epidemic model with two contagion steps, revealing a mixed-order phase transition. Critical behavior appears in mean outbreak size, not the order parameter, at the transition point.
Area of Science:
- Complex systems
- Epidemiology
- Statistical physics
Background:
- Percolation theory describes robust continuous transitions via local occupation rules.
- Generalized percolation models with cooperative occupation by multiple species exhibit discontinuous transitions.
Purpose of the Study:
- To investigate an epidemic model with two contagion steps.
- To characterize its phase transition analytically and numerically.
- To identify the nature of the phase transition and critical behaviors.
Main Methods:
- Analytical characterization of the phase transition.
- Numerical simulations of the epidemic model.
- Analysis of order parameter fluctuations and mean outbreak size.
Main Results:
- The model exhibits a discontinuous transition with an order parameter jump at r_c.
- Order parameter fluctuations do not diverge, indicating no critical behavior in the order parameter.
- Mean outbreak size shows critical behavior, diverging at r_c, similar to ordinary percolation.
Conclusions:
- The observed phase transition is classified as a mixed-order phase transition.
- Scaling relations for cascade outbreak statistics were derived for the discontinuous transition.
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