A Study On The Infectious Diseases Model Influenced By Media Reporting

Today is an information age, media spread faster and faster, the impact on the prevention and treatment of infectious diseases is becoming important. Established mathematical model of some media reports, and carries on the thorough research is also very necessary.In this paper, in order to make the model realistic we set up two types of infectious disease model of infection rate is influenced by the media, and using the stability theory knowledge to study.First, the establishment of an infectious disease model by media influence and has a segmented infection, in which part of the system is divided into two subsystems, to its research,Lambert W function using solve all the equilibrium of the system in different subsystems, and then analyze the stability of each equilibrium using stability theory of differential equations,Application exclude the presence of a Limit Cycle prove global stability of each equilibrium.For the basic reproduction number is less than one, disease-equilibrium is globally stable.Impact of media on the disease with the spread of disease is maintained at a constant level;when the basic reproduction number greater than one, endemic equilibrium in the basic reproductive number satisfying certain conditions globally stable. Numerical simulation to verify the stability of the equilibrium point.Then, it is assumed that the propagation mechanism of infectious diseases due to contact with the infected person susceptible, susceptible to enter the incubation period, and then transformed into the period of infection. A model of SEIS has established by the impact of media with the Saturating Incidence, obtain basic reproductive number based on the existence of positive equilibrium; the analysis of its characteristic equation, obtain diseasefree equilibrium is locally asymptotically stable; Using Routh-Hurwitz criterion theorem of local asymptotic stability of the endemic equilibrium under certain conditions; Using the Second additive compound matrix proved endemic equilibrium exists and is globally stable in this condition and if this condition is not satisfied when it is unstable.Through media reports that people understand the mechanism of spread of infectious diseases, as well as the intensity of infection of the disease, people can take effective measures to reduce the possibility of being infected, That is, the media coverage of the disease played a key role in preventing disease.