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Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…
In order to model an epidemic, different approaches can be adopted. Mainly, the deterministic approach and the stochastic one. Recently, a large amount of literature has been published using the two approaches. The aim of this paper is to…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
We investigate how the properties of epidemic networks change depending on the availability of different types of data on a disease outbreak. This is achieved by introducing mathematical and computational methods that estimate the…
Most of the common used models of epidemic spreading allow contaminating many neighbors of a particular node in the network. They are usually analyzed by differential equations on probability vectors. We propose a model of epidemic…
We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa $. Using very simple rules for forming such preferred degree networks, we find…
Acute infectious diseases are transmitted over networks of social contacts. Epidemic models are used to predict the spread of emergent pathogens and compare intervention strategies. Many of these models assume equal probability of contact…
Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because…
The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network,…
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
We claim that networks are created according to the priority attachment mechanism and we show a simple model which uses the priority attachment to generate both synthetic and close to empirical networks. Priority attachment is a mechanism…
When an epidemic spreads into a population, it is often unpractical or impossible to have a continuous monitoring of all subjects involved. As an alternative, algorithmic solutions can be used to infer the state of the whole population from…
Most news recommender systems try to identify users' interests and news' attributes and use them to obtain recommendations. Here we propose an adaptive model which combines similarities in users' rating patterns with epidemic-like spreading…