Related papers: Targeted Immunisation Thresholds for the Contact P…
In many real-world complex systems, individuals have many kind of interactions among them, suggesting that it is necessary to consider a layered structure framework to model systems such as social interactions. This structure can be…
We propose a new way to condition random trees, that is, condition random trees to have large maximal out-degree. Under this new conditioning, we show that conditioned critical Galton-Watson trees converge locally to size-biased trees with…
The key to our investigation is an improved (and in a sense sharp) understanding of the survival time of the contact process on star graphs. Using these results, we show that for the contact process on Galton-Watson trees, when the…
We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in…
Bipartite networks are composed of two types of nodes and there are no links between nodes of the same type. Thus the study of epidemic spread and control on such networks is relevant to sexually transmitted diseases (STDs). When entire…
Spreading phenomena are ubiquitous in nature and society. For example, disease, rumor, and information spread over underlying social and information networks. It is well known that there is no threshold for epidemic models on scale-free…
The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where…
The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected…
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of…
We study epidemic processes with immunization on very large 1-dimensional lattices, where at least some of the infections are non-local, with rates decaying as power laws p(x) ~ x^{-sigma-1} for large distances x. When starting with a…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…
The structure of social contact networks strongly influences the dynamics of epidemic diseases. In particular the scale-free structure of real-world social networks allows unlikely diseases with low infection rates to spread and become…
We study the effect of vaccination on robustness of networks against propagating attacks that obey the susceptible-infected-removed model.By extending the generating function formalism developed by Newman (2005), we analytically determine…
We propose a new method to immunize populations or computer networks against epidemics which is more efficient than any method considered before. The novelty of our method resides in the way of determining the immunization targets. First we…
Efficient testing and vaccination protocols are critical aspects of epidemic management. To study the optimal allocation of limited testing and vaccination resources in a heterogeneous contact network of interacting susceptible, recovered,…
Herd immunity is shaped not only by the infection capacity of a spreading epidemic or the contact structure of the hosting population, but also by how and under what circumstances individuals acquire immunity. Immunization strategies may…
Infection can spread easily on networks with heterogeneous degree distribution. Here, we considered targeted immunization on such networks, wherein a fraction of individuals with the highest connectivity are immunized. To quantify the…
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…