Dynamic Research Of Infectious Diseases And Information Transmission Based On Complex Networks

In recent years,infectious diseases have seriously damaged human life safety and health,and caused great damage to economic development and social stability.At the same time,illegal pyramid schemes have had an extremely negative impact on people’s social and economic life.How to effectively prevent and control the spread of infectious diseases and information diffusion has become a research hotspot in the field of complex network science.Based on the behavior and phenomenon of infectious disease transmission and pyramid schemes information transmission on complex social networks,according to the transmission mechanism of infectious diseases and pyramid schemes in reality,this paper establishes several novel dynamic models of infectious disease and pyramid schemes information transmission on scale-free network by mean field of complex network.The effects of heterogeneity of network topology,government pre-warning mechanism,quarantine mechanism and time delay on the dynamic behavior of infectious disease transmission were discussed;the impact of social network topology and government control（government anti MLM publicity and government crackdown）on the spread of pyramid schemes was analyzed;The spreading dynamic behavior was analyzed in detail.This provides a theoretical basis for controlling the spread of infectious diseases and pyramid schemes in the real world.The main work and innovations of this paper are summarized as follows:1)Taking protection and hospital quarantine measure,government pre-warning mechanism and heterogeneity of underlying networks into account,the SEAIRS（Susceptible-Exposed-Asymptomatic infected-Symptomatic infected-Recovered-Susceptible）epidemic model with protection and hospital quarantine under government pre-warning was proposed and analyzed.The basic reproduction number ₀R and two equilibriums（disease-free equilibrium and endemic equilibrium）were obtained by means of the next-generation matrix method and differential method.The endemic equilibrium is globally asymptotically stable whenR₀>1was proved;the disease-free equilibrium is globally asymptotically stable whenR₀<1and the permanence of the epidemic spreading was proved.The impact of protection and hospital quarantine measures,government pre-warning mechanism on epidemic spreading and the parameter sensitivity was studied in detail.2)After the outbreak of the“Coronavirus Disease 2019”（COVID-19）,the Chinese government took decisive and effective quarantine measures to effectively contain the further spread of the epidemic.Considering the propagation characteristics of the COVID-19 in the crowd,network topology and quarantine mechanism（Soft quarantine and Hard quarantine）,a SEAIR（Susceptible-Exposed-Asymptomatic infected-Symptomatic infected-Recovered）epidemic spreading model with time delay was proposed based on scale-free networks.The spreading dynamics of the epidemic were analyzed by the mean-field theory.Firstly,the basic reproduction numberR₀was obtained,the existence of equilibrium was proved,the relationship between network topology,quarantine mechanism（Soft quarantine and Hard quarantine）and epidemic spreading dynamics was discussed.Theoretical analysis shows that the outbreak and demise of the epidemic are completely determined by the basic reproduction number.Then,the global asymptotic stability of disease-free equilibrium and the persistence of epidemic spreading were analyzed in detail.3)With the rapid development of network and communication technology,the phenomenon of pyramid schemes becomes more serious.In order to study the influence of government management and social interaction topology on the spreading of pyramid schemes,a novel SHIPR（susceptible-hesitator-involved-punished-resister）pyramid scheme spreading model was proposed on scale-free networks.The spreading dynamics of pyramid schemes were analyzed.The basic reproduction numberR₀and equilibria are got.The local asymptotic stability of fraud-elimination equilibrium was analyzed;the global asymptotic stability of the fraud-elimination equilibrium was discussed;the global attractivity of fraud-prevailing equilibrium was proved.Theoretical analysis shows that the basic reproduction numberR₀has a great correlation with government crackdown intensity for involved individuals,the coverage rate of government anti-pyramid scheme publicity for susceptible individuals and hesitators,and social interaction topology.Finally,numerical simulations verify the theoretical analysis results.