Analysis Of The Dynamic Properties Of Infectious Disease Models With Media Coverage

The incidence of infectious diseases is influenced by various factors including population density,vaccination rates,environmental sanitation and lifestyle.With the continuous advancement of science and technology,the coverage of media is expanding rapidly.People can access a lot of information through various types of media.During an outbreak,understanding how diseases spread and how to prevent them can drive people to be more proactive and effective in preventing them.Therefore,media coverage plays an important role in the prevention and control of infectious diseases.The purpose of this paper is to study the infectious disease model with the influence of media,and to explore the dynamic properties of the model with the knowledge of dynamic system.At the same time,the influence of delayed media reporting on the infectious disease model is studied.The research project is divided into two parts.The first part establishes a class of SI infectious disease models based on the impact of media reports on disease rates.Using the second-generation matrix,the basic reproduction number of the system is calculated,and the stability of the system at two equilibrium points is analyzed.Finally,the rationality of the theory is verified by numerical simulation.The second part considers the influence of delayed media reports on disease coverage,based on the traditional disease model,the media report delay is introduced,and the media coverage volume is regarded as a single chamber to study the influence of media reports on infectious diseases with different characteristics.A SIM model is established for short-term infectious diseases that can be repeatedly infected,and a SEIRM model is established for infectious diseases with incubation period.Firstly,the system was linearized,and the corresponding characteristic equations at the disease-free equilibrium point and the endemic equilibrium point were calculated respectively.Based on the stability theory of differential equations,the stability of the system and the conditions of Hopf bifurcation near the endemic equilibrium point are analyzed,and the dynamic properties of the system are discussed.Finally,the rationality of the theory is verified by numerical simulation.