A random-walk-based epidemiological model

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.