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Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the time scales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios,…
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible…
The long-term evolution of epidemic processes depends crucially on the structure of contact networks. As empirical evidence indicates that human populations exhibit strong community organization, we investigate here how such mesoscopic…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
We investigate the relationship between complexity, information transfer and the emergence of collective behaviors, such as synchronization and nontrivial collective behavior, in a network of globally coupled chaotic maps as a simple model…
Epidemics in large complete networks is well established. In contrast, we consider epidemics in non-complete networks. We establish the fluid limit macroscopic dynamics of a multi-virus spread over a multipartite network as the number of…
In this paper, we study how interactions between populations impact epidemic spread. We extend the classical SEIR model to include both integration-based disease transmission simulation and population flow. Our model differs from existing…
In an increasingly interconnected world, a key scientific challenge is to examine mechanisms that lead to the widespread propagation of contagions, such as misinformation and pathogens, and identify risk factors that can trigger large-scale…
Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…
Many models of virus propagation in Computer Networks inspired by {\bf SIS,SIR,}\\ {\bf SEIR}, etc. epidemic disease propagation mathematical models that can be found in the epidemiology field have been proposed in the last two decades. The…
We investigate disease spreading on eight empirical data sets of human contacts (mostly proximity networks recording who is close to whom, at what time). We compare three levels of representations of these data sets: temporal networks,…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
In complex networks there are overlapping substructures or "circles" that consist of nodes belonging to multiple cohesive subgroups. Yet the role of these overlapping nodes in influence spreading processes remains underexplored. In the…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited…
How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale we consider the coherence of overall network dynamics. We show that such \emph{global coherence}…
Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties,…