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In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this…
Despite centuries of work on containment and mitigation strategies, infectious diseases are still a major problem facing humanity. This work is concerned with simulating heterogeneous contact structures and understanding how the structure…
In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the…
Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
The structure of heterogeneous networks and human mobility patterns profoundly influence the spreading of endemic diseases. In small-scale communities, individuals engage in social interactions within confined environments, such as homes…
We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large…
Memory plays a vital role in the temporal evolution of interactions of complex systems. To address the impact of memory on the temporal pattern of networks, we propose a simple preferential connection model, in which nodes have a…
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…
Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity…
We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We investigate the effects of heterogeneous and clustered contact patterns on the timescale and final size of infectious disease epidemics. The abundance of transitive relationships (the number of 3 cliques) in a network and the variance of…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…
We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen…
Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it's urgent and significant to focus on…
Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate…