Dynamic Research Of Spreading Epidemic And Information Based On Complex Networks

Since the concept of complex network was proposed,due to the unique structure and special laws of complex network,it can well describe those phenomenon of the interaction of massive individuals in various disciplines and fields such as sciences of society,sciences of life,and sciences of information.Meanwhile,the spreading behavior of various spread's objects on complex networks have a common spreading evolution mechanism and applied research value,which makes scientists never stop studying various spreading dynamics behaviors of complex networks.Among them,the spread of epidemics and the diffusion of information on complex networks has become two types of researching hot issues.This article has conducted a more in-depth study on the spread of epidemics and information on complex networks.The main innovations are as follows:1.A type of SEIQR(Susceptible-Exposed-Infected-Quarantined-Recovered)epidemic spreading dynamic model is proposed.According to the spreading characteristics of some epidemics,the behavior of epidemic spreading dynamics has been scientifically studied,and a type of epidemic spreading dynamics model has been proposed.Then,through the mean-field theory and the next generative matrix method,the basic reproductive number and two equilibriums of the model are obtained.Through the stable criterion of the Routh-Hurwitz,the local asymptotic stability of equilibriums is discussed.In addition,the global asymptotic stability of the equilibrium,persistence of epidemic spreading dynamic behavior and the global attractivity of the epidemic equilibrium are also analyzed.And the sensitivity of parameters and the basic reproductive number is analyzed.Finally,the theoretical results are verified by simulation.2.A type of SAIVQR(Susceptible-Asymptomatic-Infected-Variable-Quarantined-Recovered)epidemic spreading dynamic model with viral mutational characteristics is proposed.In order to deeply study the dynamic process of epidemic transmission with viral mutation,a novel dynamic model of epidemic transmission is proposed by considering the characteristics of viral mutation,asymptomatic characteristics,government pre-warning mechanism,quarantine characteristics and the heterogeneity of the networks.In addition,through the heterogeneous mean-field method and theoretical derivation,the basic reproductive number,the disease-free equilibrium and the epidemic equilibrium of the SAIVQR epidemic spreading dynamics model are obtained.Then,the dynamic process of epidemic spreading with viral mutational characteristics is analyzed in detail.The study found that when R₀<1,the disease-free equilibrium is globally asymptomatic stable,that is,the spread of epidemics with viral mutational characteristics will eventually disappear in the network.Moreover,when R₀>1,the spread of the epidemic will continue.In addition,preventing the virus from mutating can inhibit the spread of epidemics.3.A type of CPFB(Customer-Participant-Forwarder-Beneficiary)online group booking preferential information spreading dynamic model is proposed.Considering the impact of the products'discount rate,customer's repurchase intention and the heterogeneity of the networks on the online dissemination of preferential information,a novel dynamic model of information spreading is proposed.Through mathematical theoretical analysis,the basic reproductive number and two equilibriums of the model are obtained.The local asymptotic stability of equilibriums,global asymptotic stability of equilibriums,persistence of online group booking preferential information spreading and global attractivity of the positive equilibrium are studied.Then,the sensitivity of parameters and the basic reproductive number is analyzed.Finally,the theoretical results are verified by simulation.