Epidemic Spreading On Bipartite Scale-Free Networks

Complex networks can describe a wide variety of systems in nature and society, say, the Internet, the Wide-World-Web, science collaboration networks, portion networks, human sexual contacts networks, ecological networks, and airports networks. The ubiquity of complex networks explains why the topology and dynamics of the networks are intensively researched.Numbers of empirical results show that these networks generally possess scale-free and small-world properties. To explore their evolution mechanism and to reveal their topological properties are centered in the study of complex networks. The ultimate goal of studying complex networks is to understand how topological properties affect the dynamical processes taking place on them.In the past three decades, the modeling and analysis of sexually transmitted diseases (STDs) have received considerable attention. By combining the theory of complex networks and dynamics of heterosexual epidemic spreading, the thesis studies the evolving models, infection spreading and immune strategies on bipartite scale-free network. The studies explain some phenomenas in STDs field and may guide establishing effective immune strategy. The main contributions made in this thesis are summarized as follows:1: We propose a family of evolving models on bipartite scale-free networks. Study of the evolving mechanism of bipartite scale-free networks helps understand the dynamical process over the networks. Based on the BA model, we study the evolving of the bipartite BA-BA network, the SF-SF network with equal and non-equal scale exponents and the bipartite weighted scale-free network. Applying continuum theory and rate equation approach, the connectivity distributions of the networks are analyzed. Numerical simulation results support the theoretical results obtained.2: We present and analyze two epidemic spreading models on homogenous network. To show the importance of core group in epidemic spreading process, two SIS model are developed. The first one deals with the situation where females and males have uniform connectivity, respectively. The second one deals with the situation where females are divided into the core and general groups. The epidemic thresholds and equilibria of the two systems are obtained, and the following facts are discovered: first, infection density of the core group is remarkably larger than that of the general group. Second, the epidemic threshold of the second system is smaller than that of the first system. Moreover, the epidemic threshold decreases with the increasing of the connectivity of the core group.3: The SIS epidemiological model on bipartite scale-free networks is studied. The SIS models on BA-BA and SF-SF network are constructed for western nations, and the models on BA-Poisson and SF-Poisson network are developed for oriental nations. In the rate equation approach, it is concluded that STDs always spread in all these models. The infection densities on BA-BA network and BA-Poisson network are explicitily presented. In SF-SF network and SF-Poisson network, the ratio of the infection density of females to that of males is obtained. The conclusions imply that the ratio of infected females to males in every nation is closely related to the topology of sexual contacts network, and explain why the ratio in a western nation differs from an oriental nation. Numerical simulation results support these analytical results.4: A few immune strategies of epidemic spreading on these bipartite networks are studied. First, random edge immunity, random node immunity and random node cure are studied in homogenous network, SF-SF network and SF-Poisson network, respectively. The results show that the random immune strategies on homogenous network work and these strategies on infinite size SF-SF network and SF-Poisson network fail to control epidemic spreading. The critical value of immunized density on finite size SF-SF network and SF-Poisson network are gained. Second, the targeted immunization strategy on these networks is analyzed, and the critical values of immunized density are approximately expressed. The results show the targeted immunization strategy is a kind of effective measure dealing with the epidemic spreading on the bipartite scale-free networks.