Corpus ID: 221516128

Brownian frogs with removal: pandemics in a diffusing population

@article{Grimmett2020BrownianFW,
  title={Brownian frogs with removal: pandemics in a diffusing population},
  author={G. Grimmett and Zhongyang Li},
  journal={arXiv: Probability},
  year={2020}
}
A stochastic model of susceptible/infected/removed (SIR) type, inspired by COVID-19, is 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 random 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 $\alpha$. Two models are… Expand

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References

SHOWING 1-10 OF 35 REFERENCES
The spread of a rumor or infection in a moving population
TLDR
The principal result states that if D A = D B (so that the A- and B-particles perform the same random walk), then there exist constants 0 < C i < ∞ such that almost surely C(C 2 t) C B(t) C C (C 1 t) for all large t, where C(r) = [-r, r] d . Expand
A phase transition in a model for the spread of an infection
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B,Expand
On an epidemic model on finite graphs
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertexExpand
Asymptotic behavior of a stochastic growth process associated with a system of interacting branching random walks
We study a continuous time growth process on Zd (d⩾1) associated to the following interacting particle system: initially there is only one simple symmetric continuous time random walk of total jumpExpand
Mobile geometric graphs: detection, coverage and percolation
TLDR
This work considers the following dynamic Boolean model, and obtains precise asymptotics for detection, coverage and percolation by combining ideas from stochastic geometry, coupling and multi-scale analysis. Expand
Asymptotic behavior of the Brownian frog model
We introduce an extension of the frog model to Euclidean space and prove properties for the spread of active particles. The new geometry introduces a phase transition that does not occur for the frogExpand
Dynamic Boolean models
Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around accordingExpand
Stochastic orders and the frog model
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking allExpand
Percolation ?
572 NOTICES OF THE AMS VOLUME 53, NUMBER 5 Percolation is a simple probabilistic model which exhibits a phase transition (as we explain below). The simplest version takes place on Z2, which we viewExpand
The Shape Theorem for the Frog Model
We prove a shape theorem for a growing set of simple random walks on Zd, known as the frog model. The dynamics of this process is described as follows: There are active particles, which performExpand
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