Inhomogeneous contact processes on trees

Research output: Contribution to journalArticle

Abstract

We consider an inhomogeneous contact process on a tree double-struck T sign k of degree k, where the infection rate at any site is λ, the death rate at any site in S ⊂ double-struck T signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).

Original languageEnglish (US)
Pages (from-to)1399-1408
Number of pages10
JournalJournal of Statistical Physics
Volume88
Issue number5-6
DOIs
StatePublished - Jan 1 1997

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Contact Process
infectious diseases
death
Infection
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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "We consider an inhomogeneous contact process on a tree double-struck T sign k of degree k, where the infection rate at any site is λ, the death rate at any site in S ⊂ double-struck T signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).",
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Inhomogeneous contact processes on trees. / Wu, Chuntao Chris.

In: Journal of Statistical Physics, Vol. 88, No. 5-6, 01.01.1997, p. 1399-1408.

Research output: Contribution to journalArticle

TY - JOUR

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N2 - We consider an inhomogeneous contact process on a tree double-struck T sign k of degree k, where the infection rate at any site is λ, the death rate at any site in S ⊂ double-struck T signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).

AB - We consider an inhomogeneous contact process on a tree double-struck T sign k of degree k, where the infection rate at any site is λ, the death rate at any site in S ⊂ double-struck T signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).

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