Related papers: Contact process on a graph with communities
We investigate two homogeneous networks: the Watts-Strogatz network and the random Erdos-Renyi network, the latter with tunable clustering coefficient $C$. The network is an area of two competing contact processes, where nodes can be in two…
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…
We examine how the behaviour of high degree vertices in a network affects whether an infection spreads through communities or jumps between them. We study two stochastic susceptible-infected-recovered (SIR) processes and represent our…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in…
We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erdos and Renyi. In this theory, a network is characterized by two parameters: the size…
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of…
The symptoms of many infectious diseases influence their host to withdraw from social activity limiting their own potential to spread. Successful transmission therefore requires the onset of infectiousness to coincide with a time when its…
The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal…
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic…
We develop a theoretical framework for the study of epidemic-like social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks.…
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes…
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…
Human contact networks are constituted by a multitude of individuals and pairwise contacts among them. However, the dynamic nature, which generates the evolution of human contact networks, of contact patterns is not known yet. Here, we…
A Reed-Frost epidemic with inhomogeneous infection probabilities on a graph with prescribed degree distribution is studied. Each edge $(u,v)$ in the graph is equipped with two weights $W_{(u,v)}$ and $W_{(v,u)}$ that represent the…
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…