Localization phenomena and limits of mean-field theories in epidemic processes on networks

• Autor(a) principal: Silva, Diogo Henrique da
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: https://locus.ufv.br//handle/123456789/28031
• topic: Teoria das redes complexas (Física); Teoria de campo médio; Transformações de fase (Física estatística); Física Estatística e Termodinâmica

Complex networks have been applied to represent many real systems and investiga- tions of dynamical processes on their top are of interest, in particular, the epidemic model susceptible-infected-susceptible (SIS). In this model, theoretical descriptions of the transition from a disease-free to an endemic phase at the epidemic threshold are usually performed by means of mean-field theories. The quenched mean-field theory (QMF) takes into account the network structure regarding dynamical corre- lations. The dynamical correlations are added to QMF theory in a pairwise level in the pair-quenched mean-field theory (PQMF). We verify that, as in the QMF case, the PQMF theory can be described by the spectral properties of a Jacobian matrix which emerges within this theory. The absence of degree correlations, which allows to simplify these theories, has been considered in many studies. We analyze the effects of degree correlations on the performance of mean-field theories in determining the epidemic threshold and prevalence of the SIS model on real and synthetic networks. We investigate if there is a relation between this performance and structural and spectral properties of the network and matrices associated with the respective theories. Usually, localization in dynamical processes is investigated through eigenvectors of matrices associated to theoretical approaches near to the transition. We study this problem introducing a normalized activity vector determined by the nodal activities. We construct basis for interpreting the localization inherent to epidemic processes at the threshold and the onset of a delocalized endemic phase just above it. The method is generic and applicable to theories, stochastic simulations, real data and any network. Keywords: Complex networks. Spreading dynamics. Mean-field theories.