Dynamics Research Of Spreading Epidemic And Rumor On Complex Networks

In recent years,the study of complex networks has been paid more attention by many researchers.With the establishment of small-world network model and the scale-free network model,a wave of enthusiasm for making a research of complex networks has swept over academia.In the study,the networks relating to research mainly include:the various networks in the field of life sciences、Internet、social networks and so on.Among them,the network of epidemics propagation and the networkof information diffusion have become two hot topics in scholars.In modern society,the spread of epidemics and the spread of information have become very common transmission phenomenons,and the system in the phenomenons can all be described by complex networks.At the same time,the most typical topological structure is the scale-free property.Therefore,based on the scale-free network,this paper takes epidemic spreading and rumor spreading as the model phenomenas of the study of the spreading dynamics.The main contents and innovations of this paper include the following aspects:Firstly,considering the mechanism of isolation for close contacts,we propose a type of SOQFR（Susceptible-Osculatory-Quarantined-Free-Recovered）epidemic spreading dynamic model.Based on the current epidemic prevention and control implemented in China,we conduct a scientific analysis of the spread of epidemics.So a novel epidemic spreading dynamic model is presented.In the first pass,with the use of the mean-field theory and the next generative matrix method,the basic reproductive number and two equilibriums of the model are obtained.And then,a detailed study is done to the global asymptotic stability of epidemic-elimination equilibrium and permanence of epidemic spreading behavior of the model.In addition,we find that the intensity of government isolation for close contacts and topology of the network determine the basic reproductive number.Finally,the theoretical results are verified by simulations.Secondly,we present a type of SIVQR（Susceptible-Infected-Variable-Quarantined-Recovered）epidemic spreading dynamic model with viral mutational characteristics.We also study in detail how the mutation rate affects the epidemic spreading.Through the mathematical analyses,the basic reproductive number and two equilibriums of the established model are obtained.We also prove the globally asymptotically stable of the disease-free equilibrium and the global attractivity of endemic equilibrium.The permanence of the epidemic is also studied in detail.Finally,we verify the theoretical results through simulations and put forward some effective methods with practical value to control the epidemic spreading.Thirdly,the type of IHRTS（Ignorant-Hesitate-Rumormonger-Silent）new rumor spreading dynamic model based on the scale-free network is established.Considering the influences of the interesting degree and the coverage of truth publicity,we propose a novel rumor spreading model.The basic reproductive number and two equilibriums are solved through mathematical theoretical analysis.In addition,this paper also analyzes the relations among interesting degree,coverage of truth publicity and network heterogeneity in detail.At the same time,the global asymptotic stability of the equilibrium of the model and the permanence of rumor spreading are discussed deeply.Finally,the above theoretical results are verified by simulations.The study has demonstrated that whenR₀（27）1,the rumor-prevailing equilibrium is globally asymptomatic stable,which means that the spread of rumor will eventually disappear in the social community;when ₀R（29）1,rumor-prevailing equilibrium is globally attractive,which means that the spread of the rumor will continue.