Quarantine generated phase transition in epidemic spreading

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w_c separating a phase (w<w_c) where the disease reaches a large fraction of the population, from a phase (w >= w_c) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w_c increases with the mean degree and heterogeneity of the network. We also find that w_c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.Comment: 13 pages, 6 figure

Dynamics in online social networks

An increasing number of today's social interactions occurs using online social media as communication channels. Some online social networks have become extremely popular in the last decade. They differ among themselves in the character of the service they provide to online users. For instance, Facebook can be seen mainly as a platform for keeping in touch with close friends and relatives, Twitter is used to propagate and receive news, LinkedIn facilitates the maintenance of professional contacts, Flickr gathers amateurs and professionals of photography, etc. Albeit different, all these online platforms share an ingredient that pervades all their applications. There exists an underlying social network that allows their users to keep in touch with each other and helps to engage them in common activities or interactions leading to a better fulfillment of the service's purposes. This is the reason why these platforms share a good number of functionalities, e.g., personal communication channels, broadcasted status updates, easy one-step information sharing, news feeds exposing broadcasted content, etc. As a result, online social networks are an interesting field to study an online social behavior that seems to be generic among the different online services. Since at the bottom of these services lays a network of declared relations and the basic interactions in these platforms tend to be pairwise, a natural methodology for studying these systems is provided by network science. In this chapter we describe some of the results of research studies on the structure, dynamics and social activity in online social networks. We present them in the interdisciplinary context of network science, sociological studies and computer science.Comment: 17 pages, 4 figures, book chapte

Dynamical patterns of epidemic outbreaks in complex heterogeneous networks

We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.Comment: 13 pages, 11 figure

Spreading processes in Multilayer Networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.Comment: 21 pages, 3 figures, 4 table

The Impact of Social Curiosity on Information Spreading on Networks

Most information spreading models consider that all individuals are identical psychologically. They ignore, for instance, the curiosity level of people, which may indicate that they can be influenced to seek for information given their interest. For example, the game Pok\'emon GO spread rapidly because of the aroused curiosity among users. This paper proposes an information propagation model considering the curiosity level of each individual, which is a dynamical parameter that evolves over time. We evaluate the efficiency of our model in contrast to traditional information propagation models, like SIR or IC, and perform analysis on different types of artificial and real-world networks, like Google+, Facebook, and the United States roads map. We present a mean-field approach that reproduces with a good accuracy the evolution of macroscopic quantities, such as the density of stiflers, for the system's behavior with the curiosity. We also obtain an analytical solution of the mean-field equations that allows to predicts a transition from a phase where the information remains confined to a small number of users to a phase where it spreads over a large fraction of the population. The results indicate that the curiosity increases the information spreading in all networks as compared with the spreading without curiosity, and that this increase is larger in spatial networks than in social networks. When the curiosity is taken into account, the maximum number of informed individuals is reached close to the transition point. Since curious people are more open to a new product, concepts, and ideas, this is an important factor to be considered in propagation modeling. Our results contribute to the understanding of the interplay between diffusion process and dynamical heterogeneous transmission in social networks.Comment: 8 pages, 5 figure