Study Of Structure Of Growing Network And Pair-wise Epidemic Model On Adaptive Networks

Throughout the history of human disease,the early cholera,the plague,the Ebola virus,AIDS,SARS,avian flu,and so on,people have been suffering from the great threat of infectious diseases.Studying the spread law and development trend of infectious diseases in order to formulate effective prevention and control strategies is a common problem that people need urgently to solve.In theoretical research of infectious diseases,establishing a reasonable dynamic model to describe the spread process of infectious disease and forecasting infectious disease epidemic regularity and development trend become an effective means of researching.Complex network theory provides new tools for the study of infectious diseases and other communication problems.In addition,taking into account the behavior of individuals in daily life,for example,in order to avoid the infection,the susceptible person can break contact with the infected person,and reconnect contract with the uninfected individual,an adaptive network model can be used to describe the impact of this dynamic behavior on the spread of infectious diseases more fully.Based on these,this paper mainly gives the evolution model of multi-layer network to study its topological properties,and then based on the deficiency of traditional models,an adaptive network model is established to study the spread of infectious diseases.Chapter 1,shows the background,significance and research status of infectious diseases.And we explain the cause and the advantage that complex network can be used to study infectious diseases.In addition,several concepts on the network are given also in this chapter.Chapter 2,builds a model of growing network with friendship and contact,and the mean field model which describes the network topology.And we analyze theoretically this model when only the growth and preferential attachment mechanism are considered.Finally,some numerical simulations of studying the network topology are given,including the degree distribution,clustering coefficient and the average the nearest-neighbor degree,and draw some conclusions.Chapter 3,based on the change of network structure,shows a more accurate three-tuple approximation formula for the pair-wise model established by Gross and Shaw et al.This approximation formula can extend the previous formula which is used in the case of the neighbor obeying Poisson distribution,and make the pair-wise model more accurate.Building on these,we analyze theoretically the backward bifurcation,hopf bifurcation and other complex dynamics behaviors,which enrich the influence of dynamic network structure on the spread of infectious diseases.Chapter 4,summarizes full text and gives a prospect.