No abstract

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.

We study dynamic phenomena in a large social network of nearly 3x10;{4} individuals who interact in the large virtual world of a massive multiplayer online role playing game. On the basis of a database received from the online game server, we examine the structure of the friendship network and human dynamics. To investigate the relation between networks of acquaintances in virtual and real worlds, we carried out a survey among the players. We show that, even though the virtual network did not develop as a growing graph of an underlying network of social acquaintances in the real world, it influences it. Furthermore we find very interesting scaling laws concerning human dynamics. Our research shows how long people are interested in a single task and how much time they devote to it. Surprisingly, exponent values in both cases are close to -1 . We calculate the activity of individuals, i.e., the relative time daily devoted to interactions with others in the artificial society. Our research shows that the distribution of activity is not uniform and is highly correlated with the degree of the node, and that such human activity has a significant influence on dynamic phenomena, e.g., epidemic spreading and rumor propagation, in complex networks. We find that spreading is accelerated (an epidemic) or decelerated (a rumor) as a result of superspreaders' various behavior.