Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

Effect of the interconnected network structure on the epidemic threshold

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N×2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N×2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptible-infected-susceptible (SIS) epidemic threshold in two interconnected networks is 1/?1(A+?B), where the infection rate is ? within each of the two individual networks and ?? in the interconnected links between the two networks and ?1(A+?B) is the largest eigenvalue of the matrix A+?B. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive ?1(A+?B) using a perturbation approximation for small and large ?, the lower and upper bound for any ? as a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues and eigenvectors. We verify these approximation and boundary values for ?1(A+?B) using numerical simulations, and determine how component network features affect ?1(A+?B). We note that, given two isolated networks G1 and G2 with principal eigenvectors x and y, respectively, ?1(A+?B) tends to be higher when nodes i and j with a higher eigenvector component product xiyj are interconnected. This finding suggests essential insights into ways of designing interconnected networks to be robust against epidemics.Intelligent SystemsElectrical Engineering, Mathematics and Computer Scienc