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We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…
The disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been…
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
How does social network structure amplify or stifle behavior diffusion? Existing theory suggests that when social reinforcement makes the adoption of behavior more likely, it should spread more -- both farther and faster -- on clustered…
We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the…
We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the…
We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread…
Since social interactions have been shown to lead to symmetric clusters, we propose here that symmetries play a key role in epidemic modeling. Mathematical models on d-ary tree graphs were recently shown to be particularly effective for…
With complex networks emerging as an effective tool to tackle multidisciplinary problems, models of network generation have gained an importance of their own. These models allow us to extensively analyze the data obtained from real-world…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…