Study Of Epidemic Spreading And Immunization Strategy On Weighted Complex Networks

There are many large systems in nature that can be described by networks. Recently, complex networks that properly reflect some important features of topology and statistics in actual complex system become an effective method to research real networks. Complex networks have penetrated into many fields such as mathematical subject, life sciences, engineering and so on. Now the research on complex networks has become a very challenging subject. At present, great progress has been obtained in network topological structure and modeling, epidemic spreading, community structure, network searching, synchronization and so on. Also there are still many problems in these fields. In this paper, we discuss the epidemic spreading on complex networks.The prevalence of epidemics on social networks and frequently outbreaks of Internet worms bring on great loss and severe damage to the human beings. Therefore, the problem of epidemic spreading has always been concerned by many scientists all over the world. The complex network theory rising in recent years provides a new approach to investigate the epidemic spreading and control its outbreak. Investigating the spreading dynamics will help us better understand spreading phenomena in the real world and seek effective way to restrain harmful spreading behavior and enlarge beneficial spreading behavior. In the past, people study the virus spreading behavior mainly in the unweighted network. However, most of the real-world networks are weighted , so it is more meaningful to research the virus spreading in weighted networks. In this paper, we study the virus spreading behavior in weighted networks. The main contribution and innovative point of this dissertation is summarized as follows:Firstly, we research the virus spreading behavior in three different weighted networks with one kind of new infection mechanism. With the SI model of virus spreading being adopted and the virus spreading speed between any two nodes being positive correlation with the corresponding weight between them, the effect of different degree distributions and weight distributions on the spreading behavior in three weighted evolving networks is investigated. Study shows that with the same network size, average degree and average node strength, the more heterogeneous the intensity distribution, the faster the virus spreads, the slower the speed for achieving overall infection; meantime, the intensity distribution of newly infected nodes at different time periods is subject to exponential laws, the exponent'r'changes over time.Secondly, two kinds of infection mechanism are adopted to study immunization on BBV weighted network. It is found that the vertex betweenness-first immunization effect is better than that of the intensity-first immunization which is widely used at present, the edge betweenness-first immunization strategy is better than the other edge immunization strategies. Moreover, the effect of an immunization strategy has relation with the infection mechanism.Finally, through defining a network connectivity coefficient C, we studied several vertex and edges immunization strategies on a BBV network. Simulation study shows that in the vertex immunization strategies, target immunization strategy based on the vertex strength can strongly destroy the virus transmission network and consequently has the best immunization effect; in the edges immunization strategies, the immunization effect based on the edges betweenness is the best one among the three.