| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Sao Paulo - Brazil
[2] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | BERNOULLI; v. 27, n. 3, p. 1745-1763, AUG 2021. |
| Web of Science Citations: | 0 |
| 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 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) | |
| FAPESP's process: | 17/10555-0 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/02636-3 - Stochastic models on random environments |
| Grantee: | Pablo Almeida Gomes |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |