Local and global survival for infections with recovery

Rangel Baldasso; Alexandre Stauffer

doi:10.1016/j.spa.2023.03.008

Local and global survival for infections with recovery

Rangel Baldasso, Alexandre Stauffer

Research output: Contribution to journal › Article › peer-review

Abstract

We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Z^d with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.

Original language	English
Pages (from-to)	161-173
Number of pages	13
Journal	Stochastic Processes and their Applications
Volume	160
Early online date	14 Mar 2023
DOIs	https://doi.org/10.1016/j.spa.2023.03.008
Publication status	Published - 30 Jun 2023

Bibliographical note

Funding Information:
Supported by EPSRC FellowshipEP/N004566/1.

Keywords

math.PR
60K37, 60K35, 82C22

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2023.03.008Licence: CC BY

Cite this

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title = "Local and global survival for infections with recovery",

abstract = "We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Zd with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.",

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author = "Rangel Baldasso and Alexandre Stauffer",

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T1 - Local and global survival for infections with recovery

AU - Baldasso, Rangel

AU - Stauffer, Alexandre

N1 - Funding Information: Supported by EPSRC FellowshipEP/N004566/1.

PY - 2023/6/30

Y1 - 2023/6/30

N2 - We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Zd with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.

AB - We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Zd with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.

KW - math.PR

KW - 60K37, 60K35, 82C22

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DO - 10.1016/j.spa.2023.03.008

M3 - Article

SN - 0304-4149

VL - 160

SP - 161

EP - 173

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Local and global survival for infections with recovery

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Early Career Fellowship - Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures

Cite this

Local and global survival for infections with recovery

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Early Career Fellowship - Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures

Cite this