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Updated: Apr 15, 2026
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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
Published on: January 31, 2020
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Long-range epidemic spreading in a random environment.
Róbert Juhász1, István A Kovács1,2,3, Ferenc Iglói1,2
1Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.
Summary
This study models epidemic spreading in random environments, revealing a Griffiths phase below the epidemic threshold. The dynamical exponent continuously varies, approaching a critical value at the threshold.
Area of Science:
- Statistical Physics
- Epidemiology
- Complex Systems
Background:
- Epidemic models often simplify environments, neglecting spatial disorder and long-range interactions.
- Understanding epidemic dynamics in heterogeneous and disordered media is crucial for public health.
Purpose of the Study:
- To model and analyze long-range epidemic spreading in a quenched, disordered d-dimensional contact process.
- To investigate the dynamical behavior at and below the epidemic threshold.
Main Methods:
- Utilized a variant of the strong-disorder renormalization-group method.
- Performed Monte Carlo simulations in one and two spatial dimensions.
Main Results:
- Average survival probability decays as P(t)∼t-d/z, with logarithmic corrections.
- A Griffiths phase emerges below the threshold, with a continuously varying dynamical exponent z.
- At the threshold, infected cluster size grows as R(t)∼t1/zc and infected sites increase as Ns(t)∼(lnt)χ in 1D.
Conclusions:
- The study elucidates the complex dynamics of epidemic spreading in disordered environments.
- Identified a Griffiths phase and characterized critical behavior at the epidemic threshold.
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