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The concurrency of edges, quantified by the number of edges that share a common node at a given time point, may be an important determinant of epidemic processes in temporal networks. We propose theoretically tractable Markovian temporal…
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…
The dynamic nature of system gives rise to dynamical features of epidemic spreading, such as oscillation and bistability. In this paper, by studying the epidemic spreading in growing networks, in which susceptible nodes may adaptively break…
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 analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated random networks. We deduce the expected size of the largest vulnerable component, a network's…
We study how the spread of computer viruses, worms, and other self-replicating malware is affected by the logical topology of the network over which they propagate. We consider a model in which each host can be in one of 3 possible states -…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian…
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most…
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…
Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…
We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…
Our study is devoted to a four-compartment epidemic model of a constant population of independent random walkers. Each walker is in one of four compartments (S-susceptible, C-infected but not infectious (period of incubation), I-infected…
We present a model of contagion that unifies and generalizes existing models of the spread of social influences and micro-organismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g., a rumor or…
In this paper, we aim to understand the transient dynamics of a susceptible-infected (SI) epidemic spreading process on a large network. The SI model has been largely overlooked in the literature, while it is naturally a better fit for…