Critical value for contact processes on clusters of oriented bond percolation

Xue, Xiaofeng

doi:10.1016/j.physa.2015.12.101

Cited by 13 publications

(10 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Few results are available for the contact process on random graphs obtained from percolation-type models; see for instance [2], [7], [33] and references therein. The contact process on the supercritical random geometric graph has also been previously considered by Ménard and Singh [16], who proved that the critical infection rate is positive, and by Can [5] who obtained sharp bounds on the expected value of the extinction time on G n when the radius of connectedness goes to infinity.…”

Section: Introductionmentioning

confidence: 99%

Exponential rate for the contact process extinction time

Schapira¹,

Valesin²

2021

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Exponential rate for the contact process extinction time

Schapira¹,

Valesin²

2021

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

View full text Add to dashboard Cite

show abstract

“…In [10], Xue considers a law of large numbers of the SIR on ER graph inspired by the theory of density dependent population model introduced by Ethier and Kurtz in [2]. In [9] and [11], Xue considers the SIR epidemics on open clusters of oriented site and oriented bond percolation models on lattices as auxiliary tools to study corresponding contact processes.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic of the Critical Value of the Large-Dimensional SIR Epidemic on Clusters

Xue

2017

J Theor Probab

Self Cite

View full text Add to dashboard Cite

In this paper we are concerned with the SIR (Susceptible-Infective-Removed) epidemic on open clusters of bond percolation on the squared lattice. For the SIR model, a susceptible vertex is infected at rate proportional to the number of infective neighbors while an infective vertex becomes removed at a constant rate. A removed vertex will never be infected again. We assume that there is only one infective vertex at t = 0 and define the critical value of the model as the maximum of the infection rates with which infective vertices die out with probability one, then we show that the critical value is 1 + o(1) /(2dp) as d → +∞, where d is the dimension of the lattice and p is the probability that a given edge is open. Our result is a counterpart of the main theorem in [4] for the contact process.

show abstract

“…In [13], Xue shows that contact process on clusters of oriented bond percolation on Z d has critical value (1+o(1))/(dp) for large d, where p is probability that an given edge is open. The conclusion in [13] is easy to extend to the case where the process is with general random edge weights on oriented lattice. The bond percolation on complete graph is also known as Erdos-Renyi model (see Chapter 3 of [11]).…”

Section: Introductionmentioning

confidence: 99%

“…In [14], they extend this result to the case where the process with general random edge weights on Z + × Z d . In [13], Xue shows that contact process on clusters of oriented bond percolation on Z d has critical value (1+o(1))/(dp) for large d, where p is probability that an given edge is open. The conclusion in [13] is easy to extend to the case where the process is with general random edge weights on oriented lattice.…”

Section: Introductionmentioning

confidence: 99%

Contact Processes with Random Recovery Rates and Edge Weights on Complete Graphs

Xue

Pan

2017

J Stat Phys

Self Cite

View full text Add to dashboard Cite

In this paper we are concerned with the contact process with random recovery rates and edge weights on complete graph with n vertices. We show that the model has a critical value which is inversely proportional to the product of the mean of the edge weight and the mean of the inverse of the recovery rate. In the subcritical case, the process dies out before a moment with order O(log n) with high probability as n → +∞. In the supercritical case, the process survives at a moment with order exp{O(n)} with high probability as n → +∞. Our proof for the subcritical case is inspired by the graphical method introduce in [6]. Our proof for the supercritical case is inspired by approach introduced in [10], which deal with the case where the contact process is with random vertex weights.

show abstract

Critical value for contact processes on clusters of oriented bond percolation

Cited by 13 publications

References 19 publications

Exponential rate for the contact process extinction time

Exponential rate for the contact process extinction time

Asymptotic of the Critical Value of the Large-Dimensional SIR Epidemic on Clusters

Contact Processes with Random Recovery Rates and Edge Weights on Complete Graphs

Contact Info

Product

Resources

About