复杂网络上的病毒传播分析-计算机应用技术专业论文.docxVIP

华中科技大学硕士学位论文 华 中 科 技 大 学 硕 士 学 位 论 文 II II Abstract Complex networks are all around us. Neural networks, food web networks, social interaction networks, Internet and World Wide Web are only few examples of complex networks. Networks can represent systems composed by a large number of highly interconnected dynamical units. Apparently, these networks are different; however, they have some important common features, for example, small-world effect, scale-free property, community structure and so on. These properties of networks play an important role in spreading processes taking place on networks. The spread of computer virus, human disease outbreak, and rumor and information transmission are typical spreading processes, which can be modeled by spreading epidemics on complex networks. Firstly, the impact of scale-free properties and community structure on the spread of epidemics on networks has been considered in this article. Considering the stochastic nature of epidemic spreading, we proposed a stochastic epidemic model. In this model, there are two types of infectious contacts, namely, local contacts and global contacts. All these contacts are modeled by Possion processes. Different infectious contacts can result in different types of offspring. At early stages of epidemic spreading, the change of the number of infected individuals can be approximated with a two-type branching process. By this approximation, the basic reproduction number can be derived. We also performed individual-based simulations to study the impact of community sizes and community strength on the spreading of epidemics on scale-free networks with different degree distributions. Moreover, the infection awareness of individuals in networks and their behavioral changes have been considered. An epidemic spreading model incorporating behavioral changes has been proposed. In this model, individuals are divided into households and the defensive action toward epidemic spreading is taken by the househol