Contact process under heavy-tailed renewals on finite graphs

Autor(es)

Fontes, Luiz Renato ^[1] ; Gomes, Pablo Almeida ^[2] ; Sanchis, Remy ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Sao Paulo - Brazil

^[2] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BERNOULLI; v. 27, n. 3, p. 1745-1763, AUG 2021.
• Citações Web of Science: 0

Resumo

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 x is an element of V, 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 lambda > 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 mu such that mu(t, infinity) = t(-alpha)L(t), where 1/2 < alpha < 1 and L(center dot) 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 vertical bar V vertical bar < 2 + (2 alpha - 1)/{[}(1 - alpha)(2 - alpha)], then the infection does not survive for any lambda; and if vertical bar V vertical bar > 1/(1 - alpha), then, for every lambda, the infection has positive probability to survive. (AU)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 20/02636-3 - Modelos estocásticos em ambientes aleatórios
• Beneficiário: Pablo Almeida Gomes
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado