Dynamics On Complex Networks

Based on the small-world and scale-free properties, epidemics can spread quickly and can be transmitted globally. There is much more interest in the question of how to immunize a social, a population, or a computer network, such as the internet network, with a minimal number of immunization doses. This question is very important since in many cases the number of immunization doses is very limited, or costs an arm and a leg. To achieve this goal, many immunization strategies have be proposed, ranging from local strategies, such as uniform immunization and acquaintance immunization, to global strategies, such as targeted immunization and EGP immunization. Many network models have also been proposed to exhibit real networks'properties, such as ER networks, WS small world networks, BA scale free networks and local-world evolving networks and so on.At different situations, different immunization strategies were proposed: Based on the rich-club phenomenon, which means that important nodes prefer to connect earth other, the Rich-Club phenomenon based search immunization strategy, via the Breadth-First algorithm to search and then immunize important nodes, was proposed. The immunize algorithm can effectively reduce the heterogeneity propriety; Based on the connection between edges and important nodes, an immunization edges strategy is proposed. The basic idea of this strategy is first to rank the importance of nodes and then remove edges between important nodes. In order to lengthen the mean path of important nodes, edges between its'common neighbors are also deleted; Based on the experiment of six degrees of separation, local search immunization strategy in inhomogeneous networks is also proposed, which is first to search utilizing high degree nodes and then immunize important nodes. Three immunization strategies are tested in WS small world networks, BA scale free networks or real networks, using SIS or SIR epidemic spreading model. Experiments exhibit that these algorithms can effectively reduce the immunization threshold and raise the spreading threshold compared to existing strategies, such as targeted immunizations, acquaintance immunizations etc.Studies of epidemic spreading focus on epidemic spreading models, the outbreak threshold, immunization strategies, and prediction of spreading and so on, but connections between edges and spreading speed are seldom analyzed. Edges belong to different coefficients affect epidemic spreading speed differently. Such as when epidemics spread through one clique to another clique, spreading speeds speed up. Although edges of undirected networks are undirected, spreading direction exists during the spreading process.Spreading speed is evaluated through the number of related infected nodes, which appears after m time step. The connection between jaccard coefficient and spreading speeds, and the connection between degree product and spreading speed are tested. If the jaccard coefficient is less than one, the spreading speed increases with jaccard coefficient's raise. If edges, which can greatly increase the spreading speed, are removed, the mean spreading speed slows down. Jaccard coefficient and degree product are corrected with considering spreading direction.