Epidemic And Immunization Strategy On Complex Networks

The content of Complex Networks research is extensive and involves in various disciplines. In recent years, the spreading mechanism and its dynamic got widely studied as an important branch of Complex Networks. Spread phenomena are universal in nature and activities of human beings, and are related closely to people's everyday life. The outbreak of internet virus and the spread of human diseases could both be regarded as propagations under certain rules in complex networks. As plenty of outbreaks of infectious diseases or computer viruses have significantly impacted human life in history, immunization strategies are brought by researchers to avoid or relive such damages. For scale-free networks, as the spread threshold is zero, virus could quickly spread and reach steady state if only virus have positive spread probability, which implying the fragility of scale-free networks. Studies of recent years discovered that most real network topologies own a scale free feature. Thus, finding a better immune strategy becomes particularly important for a network.Different propagation models are employed to study real networks with different spreading modes; classical models include Susceptible-Infected (SI) Model, Susceptible-Infected-Susceptible (SIS) Model, Susceptible-Infected-Removed (SIR) Model and Susceptible-Exposed--Infected-Removed (SEIR) Model. Scale-free networks are fragile for virus spread and attacks; this necessitates affiant immune strategy for a network. Typical strategies being recently studied include random immunization, acquaintance immunization, target immunization, and a variety of improved strategies. This thesis studied the topology of networks, brought two improved immune strategies:secondary sort strategy and dynamic strategy. The detailed work is as follows:(1) The development process of complex networks was reviewed, its curr ent situation was summarized, and the meaning of immune strategies were anal ysed.(2) Then, we firstly introduced concepts of complex network and its degree distribution, average path length and clustering coefficient. Secondly, we talked about three spreading modes:SI model, SIS model and SIR model, and gave differential equations of their transmission of the virus. Under SIS model, we researched the spread threshold of uniform networks and scale-free networks. Finally, we discussed three immune strategies:random immunization, target immunization, acquaintance immunization, examined the differences between these three immune strategies, and evaluated the advantage and disadvantage for each strategy.(3) We chose the hep-th network from Newman for study. The original network is of certain unconnectedness, so network data was manipulated and its maximal connected sub graphs--HEP network--was returned.(4) The three characteristics of HEP network were analyzed:its degree distribution, average path length and clustering coefficient. Simulations were taken under SI Model, SIS Model and SIR Model, for their different virus propagation processes.(5) This thesis considered another situation, nodes of low degree would be connected to core nodes of network, and this increased their importance. New methods of evaluating node's importance were proposed to give such nodes certain precedence. Based on this dynamic strategy was introduced. After plenty of experiments and modifications, we found that infection density was reduced through dynamics strategy and risks of virus were lessened.(6) Analysis on degree distribution of HEP revealed that there are lots of nodes with a same degree. How to define the immune priority of identically degreed nodes? It's noticed that nodes connected to high degreed neighbors should be more important. Based on this the secondary sort strategy was introduced. Comparative experiments of secondary sort strategy and target strategy proved that, the former efficiently reduced the rate of virus outbreak and infection density of network, thus it's more effective.