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August 2021 Contact process under heavy-tailed renewals on finite graphs
Luiz Renato Fontes, Pablo Almeida Gomes, Remy Sanchis
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Bernoulli 27(3): 1745-1763 (August 2021). DOI: 10.3150/20-BEJ1290

Abstract

We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site xV, and it can be infected or healthy; the infection propagates to healthy neighbors just as in the usual contact process, according to independent exponential times with a fixed rate λ>0; however, the recovery times for an individual are given by the points of a renewal process attached to its timeline, whose waiting times have distribution μ such that μ(t,)=tαL(t), where 1/2<α<1 and L(·) is a slowly varying function; the renewal processes are assumed to be independent for different sites. We show that, starting with a single infected individual, if |V|<2+(2α1)/[(1α)(2α)], then the infection does not survive for any λ; and if |V|>1/(1α), then, for every λ, the infection has positive probability to survive.

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Luiz Renato Fontes. Pablo Almeida Gomes. Remy Sanchis. "Contact process under heavy-tailed renewals on finite graphs." Bernoulli 27 (3) 1745 - 1763, August 2021. https://doi.org/10.3150/20-BEJ1290

Information

Received: 1 February 2020; Revised: 1 October 2020; Published: August 2021
First available in Project Euclid: 10 May 2021

Digital Object Identifier: 10.3150/20-BEJ1290

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 3 • August 2021
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