Study On Infectious Disease Model With Delayed Media Reporting

At present,human beings are living in an era of information sharing on the Internet.Connecting the Internet can search a large number of relevant information,which provides a convenient channel for all aspects of human information.Just as an infectious disease has broken out,the coverage of disease symptoms and protective measures by the mass media will promptly arouse people's attention to the disease and actively prevent it,therefore,media awareness reports are conducive to people's prevention and control of infectious diseases,thence,on the basis of previous research work,this paper constructs two types of time-delay infectious disease models with media reports to analyze the impact of media awareness reports on the spread of infectious diseases.Firstly,the SIS time-delay model with media saturation incidence was established,The effect of media saturation function on the reduction of infectious rate is studied to characterize the impact of media coverage on the dynamics of infectious diseases.Based on the analysis of the qualitative and stability theory of differential equations,when R₀?1,the disease-free equilibrium is locally asymptotically stable and globally asymptotically stable;when R₀?1,there was only one equilibrium point for endemic diseases.When ?=0,it is locally asymptotically stable,when ??0,When the parameters satisfy certain conditions and ? crosses critical initial value ?₀,periodic oscillation and instability will occur at the equilibrium point of endemic diseases,the Hopf branch appears;The theoretical analysis was verified by numerical simulation using Matlab software,which showed that the media awareness report had a certain influence on the spread of the disease.Secondly,a kind of time-delay infectious disease model with media reports was established,and the population was divided into two types of people who were conscious and unconscious of the disease,the theoretical analysis obtained the basic regeneration number and existence of balance point;By using the characteristic equation analysis at the disease-free equilibrium point,it is found that the disease-free equilibrium point is locally asymptotically stable if R₀?1,by constructing Liapunov function,it is found that the disease-free equilibrium is globally asymptotically stable if R₀?1;According to the Hurwitz criterion,the condition that the positive equilibrium point is locally asymptotic is obtained,the condition of generating Hopf branch at the positive equilibrium point with time-delay model is obtained;The theoretical analysis results are verified by numerical simulation.Finally,through the media's extensive coverage of various precautions for the disease,people who receive the report will have a preventive treatment for the disease,which is divided into conscious people,so the rate of infection will be reduced;the people who do not receive the reports of diseases have no preventive psychology,that is,they are divided into unconscious groups,and the incidence of diseases of these people is relatively high.So it can be seen that media coverage is of great significance for disease control.