Local survival of spread of infection among biased random walks

Abstract

We study infection spread among biased random walks on ${\mathbb{Z}}^d$. The random walks move independently and an infected particle is placed at the origin at time zero. Infection spreads instantaneously when particles share the same site and there is no recovery. If the initial density of particles is small enough, the infected cloud travels in the direction of the bias of the random walks, implying that the infection does not survive locally. When the density is large, the infection spreads to the whole ${\mathbb{Z}}^d$. The proofs rely on two different techniques. For the small density case, we use a description of the infected cloud through genealogical paths, while the large density case relies on a renormalization scheme.

arXiv comment31 pages, 4 figures. Manuscript matching published version

References in corpus (10)

• The spread of a rumor or infection in a moving population
• Soft local times and decoupling of random interlacements
• The shape theorem for the frog model with random initial configuration
• Mobile Geometric Graphs, and Detection and Communication Problems in Mobile Wireless Networks
• Space-time percolation and detection by mobile nodes
• How can a clairvoyant particle escape the exclusion process?
• Multi-scale Lipschitz percolation of increasing events for Poisson random walks
• Front propagation in an exclusion one-dimensional reactive dynamics
• Random walks in random conductances: decoupling and spread of infection
• Spread of an infection on the zero range process

Cited by in corpus (1)

• Local and global survival for infections with recovery