Contact process under renewals I

Author(s)

Fontes, Luiz Renato G. ^[1] ; Marchetti, Domingos H. U. ^[2] ; Mountford, Thomas S. ^[3] ; Vares, Maria Eulalia ^[4]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

^[2] Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil

^[3] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne - Switzerland

^[4] Univ Fed Rio de Janeiro, Inst Matemat, Rio De Janeiro, RJ - Brazil

• Document type: Journal article
• Source: Stochastic Processes and their Applications; v. 129, n. 8, p. 2903-2911, AUG 2019.
• Web of Science Citations: 2

Abstract

We investigate a non-Markovian analogue of the Harris contact process in Z(d): an individual is attached to each site x is an element of Z(d), and it can be infected or healthy; the infection propagates to healthy neighbours just as in the usual contact process, according to independent exponential times with a fixed rate lambda; nevertheless, the possible recovery times for an individual are given by the points of a renewal process with heavy tail; the renewal processes are assumed to be independent for different sites. We show that the resulting processes have a critical value equal to zero. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants