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Infection fronts in randomly varying transmission-rate media.

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This study reveals that infection front propagation in spatial SIR models is sensitive to transmission rate randomness. Uniform transmission increases front harmfulness, impacting vaccination strategies and revealing universal geometric features compatible with KPZ universality.

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Area of Science:

  • Epidemiology
  • Statistical Physics
  • Computational Biology

Background:

  • The spatial SIR model is crucial for understanding infectious disease dynamics.
  • Quenched random transmission rates introduce complex behaviors in infection spread.
  • Mean-field homogenization often overestimates critical transmission rates.

Purpose of the Study:

  • To numerically investigate infection front geometry and transport in a 2D spatial SIR model.
  • To analyze the impact of short-range correlated quenched random transmission rates.
  • To compare findings with theoretical models like Kardar-Parisi-Zhang (KPZ).

Main Methods:

  • Numerical simulations of the spatial SIR model in two dimensions.
  • Incorporation of short-range correlated quenched random transmission rates.
  • Analysis of infection front velocity, profile, and harmfulness.

Main Results:

  • Critical transmission rate for steady-state propagation is overestimated by naive mean-field homogenization.
  • Front velocity, profile, and harmfulness depend on randomness details.
  • Higher uniformity in transmission rates leads to increased front harmfulness.
  • Front geometry exhibits universal features, with roughness exponent α≈0.42±0.10 and dynamical exponent z≈1.6±0.10.
  • KPZ term and disorder-induced noise are present with kinematic origin.

Conclusions:

  • Randomness in transmission rates significantly affects infection spread dynamics.
  • Uniformity in transmission can enhance disease spread, informing vaccination strategies.
  • The observed front dynamics align with the 1D KPZ universality class, suggesting robust universal behaviors.