Epidemic processes and diffusion on networks: analytical and computational aproaches

• Ano de defesa: 2015
• Autor(a) principal: Mata, Angélica Sousa da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Viçosa
• Palavras-chave em Português: Física estatística; Epidemias; Transformação de fase (Física estatística); Teoria de campos (Física); Física da Matéria Condensada
• Link de acesso: http://www.locus.ufv.br/handle/123456789/6343

A field of outstanding interest in Statistical Physics is the investigation of dynamical processes on complex networks. This thesis is devoted to explore the behavior of epidemic dynamics running on heterogeneous networks. We improved analytical approaches - quenched and heterogeneous mean-field theories - by means of pair approximations, which explicitly take into account dynam- ical correlations between connected vertices. These approaches yield more accurate predictions of the epidemic thresholds in the susceptible-infected-susceptible (SIS) model and the critical expo- nents associated to the absorbing state phase transition of the contact process (CP) obtained through finite-size scaling. These approaches can be applied to dynamical processes on networks in gen- eral providing a profitable strategy to analytically assess and fine-tune theoretical corrections. We also investigated the SIS dynamics on random networks having a power law degree distribution (P (k) ∼ k −γ ), with exponent γ > 3, since the existence or absence of a finite threshold involving an endemic phase has been target of a recent and intense investigation. We found that this model on a single network can exhibit multiple transitions involving localized epidemics and our numerical analysis indicates that the transition to the endemic state occurs at a finite threshold. Our analy- sis points out that competing mean-field theories are, in fact, complementary since they describe different epidemic thresholds which can concomitantly emerge in a single network. Finally, we also investigated the diffusion processes on temporal networks by means of a random walk. We analyzed this dynamic theoretically by means of a mapping to Bouchaud’s trap model and using numerical simulations. We found evidence of aging behavior in the random walk relaxation.