Epidemic Spreading On Complex Networks

Since the discovery of small-world and scale-free network, the complex net-work has become one of the hot topics among the scientific research areas nowa-days. It covers varies areas such as biology, economy, linguistics and sociology,showing the vitality as a promising crossing discipline. We here consider oneof its application in sociology, i.e., the epidemic spreading on the networks. Inthis thesis, we present three research contents:the epidemic spreading on a two-layered network, how the contagion at links influences epidemic spreading andepidemic spreading with information-driven vaccination. The thesis is organizedas follows: The first chapter is an introduction. In this section, we briefly introduce theresearch background, the motivation, and our works. The second chapter is a preparation for the further reading, we introduce thebasic concepts of networks and present some typical network models. Besides,some classical epidemic models and vaccination methods are also introduced. In the third chapter, In view of the huge investments into the constructionof high speed rails systems in US, Japan, and China, we present a two-layeredrailway-local area traveling network model and study the epidemic spreading onsuch network. We find that, comparing to a single ER network, the two-layeredmodel will lead to a faster initial infection and a more severe level of infection inthe steady state. That is mainly because of the stations where can gather manytraveling individuals. However, the higher speed trains, which stop at fewerstations and each station could serve a bigger local area, will help suppressesthe level of infection. These results can also be extended to other two-layered ormulti-layered transportation systems, like airports-local area traveling networket al., and are of significant help to understand how the modern transportation systems can influence the epidemic spreading.In the fourth chapter, based on the observation that people are very likely to be infected when they are traveling, which is totally neglected by the classi-cal "reaction-diffusion" model, we present a traveling-contagion model to dis-cuss the epidemic spreading. In this model, people are distributed both at the nodes and the links. Considering the density of travelers in transportation is much higher than that in local areas, we let the contacting rate is larger at the links. We consider three typical diffusion processes, i.e., random diffusion, pref-erential diffusion, and objective traveling, and found that the contagion at links can significantly accelerate the epidemic spreading. Moreover, the diffusion pro-cesses will also influence the results. These results provide rich suggestions for the health authorities to respond the future outbreaks of epidemics.In the fifth chapter, considering a person has crisis awareness which probably arisen by the outside information in real lives, we present an information-driven vaccination model to study the epidemic spreading. We introduce two parame-ters to quantitatively characterize the information amount and the personal crisis awareness. One is the information creation rate λ and the other is the information sensitivity η. We find that when both λ and77are large, the epidemic spreading can be suppressed effectively. More interestingly, the needed vaccine is also very less. This is good news for the poor countries and regions with limited resource.In the sixth chapter, we summarize the thesis and give an outlook of the future study.