Conjoining Speeds up Information Diffusion in Overlaying Social-Physical Networks

We study the diffusion of information in an overlaying social-physical network. Specifically, we consider the following set-up: There is a physical information network where information spreads amongst people through conventional communication media (e.g., face-to-face communication, phone calls), and conjoint to this physical network, there are online social networks where information spreads via web sites such as Facebook, Twitter, FriendFeed, YouTube, etc. We quantify the size and the critical threshold of information epidemics in this conjoint social-physical network by assuming that information diffuses according to the SIR epidemic model. One interesting finding is that even if there is no percolation in the individual networks, percolation (i.e., information epidemics) can take place in the conjoint social-physical network. We also show, both analytically and experimentally, that the fraction of individuals who receive an item of information (started from an arbitrary node) is significantly larger in the conjoint social-physical network case, as compared to the case where the networks are disjoint. These findings reveal that conjoining the physical network with online social networks can have a dramatic impact on the speed and scale of information diffusion.Comment: 14 pages, 4 figure

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Epidemic model with isolation in multilayer networks

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.We thank the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. LGAZ and LAB wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio

Epidemic Model with Isolation in Multilayer Networks

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isolation parameter to measure the effect of isolating infected individuals from both layers during an isolation period. We call this process the Susceptible-Infected-Isolated-Recovered ($SI_IR$) model. The isolation reduces the transmission of the disease because the time in which infection can spread is reduced. In this scenario we find that the epidemic threshold increases with the isolation period and the isolation parameter. When the isolation period is maximum there is a threshold for the isolation parameter above which the disease never becomes an epidemic. We also find that epidemic models, like $SIR$ overestimate the theoretical risk of infection. Finally, our model may provide a foundation for future research to study the temporal evolution of the disease calibrating our model with real data.Comment: 18 pages, 5 figures.Accepted in Scientific Report