Simulações quase estacionárias do processo de contato em redes complexas

• Autor(a) principal: Ferreira, Ronan Silva
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4234
• topic: Física estatística; Redes complexas; Trasnsição de fase; Statistical Physics; Complex networks; Phase transition; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA

The study of the structure and correlations properties among interconnected agents on complex networks has attracted the attention of the Statistical Physics community through investigation of dynamical process on this topologies. These investigations have opened discussions in the literature concerning on the validity of the predictions from mean field (MF) approaches, when these results are compared with those obtained from computer simulations. The contact process (CP) is a toy model for the epidemic spreading on a population. Using the complex network approach, we identify each individual as a network node, while their relations are represented by links among them. In the CP model, each individual may be infected or not, with a probability depending on the epidemic infection rate. This rate can lead to the dissemination of the epidemic at long times or its complete eradication, given that exists also a chance to the infected individuals become healthy, determining a phase free of the disease (absorbing phase) and other in which the disease persists (active). The computer implementation of the CP and different network topologies allows us to compare our results with those predicted by MF theory found in the literature. The main aim of the present work was the study of the finite size scaling theory for the PC in the complex network proposed by Watts-Strogatz (WS) and by Barabási-Albert (BA) by quasistationary simulations. This study provided a set of critical exponents for the characterization on the phase transition absorbing-active on BA network and also on two topologies found at the WS model, namely, small world and random. Although the predictions made by MF approaches have been verified for this set of critical exponents, the phase transition rates obtained was not predicted correctly. This fact is on contrast with others epidemic models, such as SIS and SIR, already studied in the literature on these complex networks.