Wilson renormalization of a reaction-diffusion process

Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants D_A and D_B. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/\tau). The propagation of the epidemic therefore couples to the fluctuations in...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 1997-06
Main Authors: F van Wijland, Oerding, K, Hilhorst, H J
Format: Article
Language:English
Subjects:
Dependence
Diffusion
Epidemics
Extinction
Field theory
Population density
Variations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants D_A and D_B. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/\tau). The propagation of the epidemic therefore couples to the fluctuations in the total population density. Global extinction occurs below a critical value \rho_{c} of the spatially averaged total density. The epidemic evolves as the diffusion--reaction--decay process A + B --> 2B, B --> A , for which we write down the field theory. The stationary state properties of this theory when D_A=D_B were obtained by Kree et al. The critical behavior for D_A
ISSN:2331-8422
DOI:10.48550/arxiv.9706197