Analysis Of Propagation Dynamics On Coupled Networks

In 1940 s,information theory was founded,pointing out that information is ubiquitous.Along with the social civilization and progressive popularity of Internet,information is becoming more and more diverse.Since the emergence of information and generalized information----the viruses,it has been increasingly important to detect and analyze the propagation mechanism of information and therefore make use of information propagation to control and prevent virus contagion.In recent years,the research on this issue,has become an important area,called social communication.In this dissertation,we investigate the evolutionary dynamics of propagation of viruses or information on coupled networks.Based on complex networks theory,we establish dynamic models for viruses or information,and adopt dynamic theories and methods to analyze the stablitiy,persistence and sensitivity for the models.Furthermore,we probe into the evolutionary dynamics of viruses or information spread on coupled networks to seek suitable countermeasures for emerging viruses.Then we explore the edge-based contagion of a type of file virus on a tripartite graph,and find out efficient meaures to control the contagion.Finally,we draw on the real data,the parameter estimation and sensitivity analysis to study the effects of the demographic information on the spread of viruses on regular network.The dissertation is organized as follows.In Chapter 1,we present an introduction to the background and give emphasis on the importance of the information or virus propagation.We give a brief explanation for several terms relevant to our work,and list the highlight and summary for each chapter.In Chapter 2,we comprehensively take into account the human behavior and demographic factors in large spatiotemporal scales,including births,deaths,migration and short-time travel,to study the virus propagation on complex networks with two communities.By establishing and analyzing a temporally varying Susceptible-Infected-Susceptible(SIS)model on networks,we have performed numerical simulations to find out the impact of parameters on the infected number and the basic reproduction number.We give some measures to prevent the virus spread on community networks.Taking into account the differences between communities,we further study the effect of different immigration and emigration scenarios on the virus spread.Sensitivity analysis is performed to provide control measures.In Chapter 3,we develop a dynamic model for the propagation of the virus and the information on coupled networks.We fully explore the interactions of virus spread and information spread,and unveil the significant role of information spread on the virus spread.Moreover,we propose an information propagation model based on the awareness level.The dynamic analysis and numerical simulations are carried out to obtain the basic reproduction number and the stabilities of equilibria.Finally,we perform sensitivity analysis and give some intervention strategies.In Chapter 4,to study the transmission of a type of file virus,we construct a tripartite graph consisting of web pages,computers and removable disks.And based on the tripartite graph and effective connections along which infections take place,we derive a deterministic dynamic pairwise model including 12 differential equations.By means of analysis and simulations,we give precautions to the transmission of file viruses.In Chapter 5,based on the statistics of hand,foot,and mouth disease(HFMD)in China,we take into account the demographic information and school terms and school breaks to propose a dynamic model for the virus spread.The model is analyzed,showing that the model can well fit the periodic outbreaks,especially the periodic ripples around September.Besides,we predict the spread of hand,foot,and mouth disease in China and provide efficient approaches to control and prevent it.In the last Chapter,we present the conclusion and point out potentials to further improve each model,which deserve more efforts in the future.