Abstract
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph : an individual is attached to each site , 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 ; 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 , where and 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 , then the infection does not survive for any λ; and if , then, for every λ, the infection has positive probability to survive.
Citation
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
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