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A random-walk-based epidemiological model.

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This study uses random walkers on a lattice to model epidemic spread, revealing complex dynamics beyond traditional models. Spatial fluctuations influence the basic reproductive number, offering new insights into contagion transmission and scaling behavior.

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Area of Science:

  • Epidemiology
  • Statistical Physics
  • Computational Modeling

Background:

  • Traditional epidemic models often assume well-mixed populations, which may not capture real-world spatial complexities.
  • Understanding spatio-temporal epidemic dynamics is crucial for effective public health interventions.

Purpose of the Study:

  • To explore epidemic spread using a random-walk model on a 2D lattice.
  • To investigate the influence of spatial fluctuations on epidemic dynamics and the basic reproductive number.
  • To characterize long-term epidemic behaviors and scaling in the critical region.

Main Methods:

  • Simulations of random walkers on a two-dimensional square lattice.
  • Numerical calculation of phase diagrams to identify long-term behaviors.
  • Analysis of the functional dependence of the basic reproductive number on model parameters.
  • Study of space and time scaling in the critical region.

Main Results:

  • The random-walk model exhibits non-trivial epidemic dynamics compared to well-mixed models.
  • A novel expression for the basic reproductive number was derived, highlighting the role of spatial fluctuations.
  • Inter-regional contagion transmission was simulated and analyzed.
  • Scaling behavior in the critical region was found to be consistent with directed-percolation universality.

Conclusions:

  • Random-walk models provide a more nuanced understanding of epidemic spatio-temporal growth.
  • Spatial effects significantly impact epidemic parameters like the basic reproductive number.
  • The findings suggest a connection to directed-percolation universality, offering a framework for analyzing epidemic scaling.