Epidemic Spreading On Complex Networks With Multiple Transmission Factors And Its Immunization Strategies

Both the prevalence of epidemics among the crowd and the rampancy of them on the information networks bring on great loss to the human beings. Therefore, studying the transmission mechanism of epidemics and then adopting measures to effectively control their spread have important practical significance. Moreover, many social, biological, and communication systems in real life can be properly deseribed by complex networks. The development of complex network theory for people to understanding the propagation characteristics of epidemics and defensing their spreading provides a new method. In recent years, using the complex network theory to investigate the spreading dynamic behaviors of epidemics is more and more concerned. With the gradual deepening of the study of complex network transmission dynamics, people have achieved fruitful results as well as find that the propagation characteristics of epidemics will be affected by factors of transmission, such as spreading delay, infective medium, imperfect immunization and network traffic flow, etc. Based on the survey of research status of epidemic spreading on complex networks, and enlightened by the existing research work, the dissertation focuses on the impact of the above transmission factors on the complex networks transmission dynamic behaviors. Furthermore, according to the propagation mechanism of epidemics abtained by researching, this dissertation discusses the related immunization strategies, and proposes two new immune mechanisms which can effectively control epidemic spreading on networks. The main research work of the dissertation is as follows:1. Based on the mean-field theory, the dissertation studies the influence of both infective medium and spreading delay to epidemic spreading on the networks. Research shows that the existence of both infective medium and spreading delay can significantly enhance the risk of outbreak of epidemics and accelerate the epidemic spreading in the networks. For a given propagation rate, it is also found that the epidemic prevalence on the homogeneous network varies logarithmically with infection probability of infective medium and spreading delay respectively, and the epidemic prevalence on the scale-free network has a power-law relation with infection probability of infective medium, but a linear relation with spreading delay.Moreover, based on the cellular automata, the dissertation further studies how the spreading delay influences epidemic spreading on the networks. Research shows that both the epidemic prevalence and the propagation velocity increase obviously with the spreading delay becoming large. It is also found that the cellular automata model the dissertation proposed in this dissertation can describe not only the average propagation tendency of epidemics, but also the dynamic evolution process over time of epidemics and the probability events such as outbreak and extinction of epidemics, and thus can overcome the limitations of the differential equation model based on mean-field method that describes only the average transmitting tendency of epidemics. Meanwhile, the dissertation presents some suggestions on how to effectively control the propagation of epidemics.2. Based on the mean-field theory, the dissertation investigates the influence of network traffic flow on the spreading behaviors of epidemics on the networks, and proposes an improved acquaintance immunization mechanism. Research shows that as the network traffic flow increases, the epidemic spreading in the networks is obviously accelerated, and therefore the risk of outbreak of epidemics is significantly enhanced. We also find that considering the influence of traffic flow, the random immunization can hardly reduce the spreading velocity of epidemics if the density of vaccinated nodes is small. However, the targeted immunization can sharply depress the epidemic spreading even only a tiny fraction of nodes are vaccinated, and the effects of immunizing the most highly connected nodes and vaccinating the nodes with the largest betweenness are almost the same. Moreover, if the network global information is unknown, comparing with the classical acquaintance immunization strategy, the one proposed in this dissertation can be used to obtain better immune effect.3. The imperfect immunization on complex networks includes immune failure and immune invalidity. Based on mean-field theory, the dissertation studies the effect of both immune failure and immune invalidity to epidemic spreading on the networks. The research shows that the immune failure and immune invalidity can significantly reduce the epidemic threshold and enhance the epidemic prevalence in the networks. According to the relationship among epidemic threshold, immune density of nodes, immune success rate and immune invalid rate, the dissertation presents some suggestions on how to effectively control the propagation of epidemics. In order to abtain the desired immune effects, the dissertation gives the expression of the immune node density in the networks.4. Based on complex network theory, the dissertation proposes a new evolving network model among the cluster heads to study the impact of node failure on the performance of wireless sensor networks. Based on the proposed model, the dissertation discusses the epidemic spreading and its immunization strategies, and presents a new immune mechanism. Research shows that such evolving network not only has strong fault tolerance, but also can effectively avoid node's premature death caused by the rapid energy depletion. We also show that if the global network information is unknown, the proposed immunization strategies in this dissertation can obtain better immune effect than the random immunization and acquaintance immunization strategies.