Repository logo
 

Brownian snails with removal: epidemics in diffusing populations*

Published version
Peer-reviewed

Repository DOI


Type

Article

Change log

Authors

Grimmett, GR 
Li, Z 

Abstract

Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously according to independent diffusion processes. The disease may pass from an infected individual to an uninfected individual when they are sufficiently close. Infected individuals are permanently removed at some given rate α. Such processes are reminiscent of so-called frog models, but differ through the action of removal, as well as the fact that frogs jump whereas snails slither. Two models are studied here, termed the delayed diffusion' and the diffusion' models. In the first, individuals are stationary until they are infected, at which time they begin to move; in the second, all individuals start to move at the initial time 0. Using a perturbative argument, conditions are established under which the disease infects a.s. only finitely many individuals. It is proved for the delayed diffusion model that there exists a critical value αc∈(0,) for the survival of the epidemic.

Description

Keywords

math.PR, math.PR, 60K35, 60G15

Journal Title

Electronic Journal of Probability

Conference Name

Journal ISSN

1083-6489
1083-6489

Volume Title

27

Publisher

Institute of Mathematical Statistics