Study On The Dynamics Of The Filippov Infectious Disease Based On Media Effects

Emerging infectious diseases pose a great threat to public health.As an im-portant channel of disease information dissemination,media has affected people’s cognition of disease to a certain extent.In particular,media coverage can change people’s behavior,and reduce the spread of diseases.At the same time,media coverage can also have a significant impact on the implementation of public con-trol measures.It can be seen that media coverage plays a crucial role in the spread of diseases and should be considered in infectious disease models.Therefore,it is necessary to study the impact of media coverage on the spread of diseases.Based on the classical infectious disease model,this paper studies the impact of media on infectious disease by considering threshold strategy.The main research results of this paper are as follows:1.Considering that media coverage is intermittent and does not appear from the beginning of the infectious disease and continues throughout.Therefore,we establish a Filippov infectious disease model with nonlinear incidence to describe the impact of media in the transmission of infectious diseases.Our proposed model extends the existing model by introducing a threshold strategy to describe the impact of media coverage once the number of infected individuals exceeds the threshold.At the same time,we give the stability of the system equilibrium point,the boundary equilibrium bifurcation and the global dynamics.The system shows complex dynamic behavior and finally stabilizes at the equilibrium point of the system or pseudo-equilibrium point.In addition,the numerical simulation results show that selecting appropriate threshold and control intensity can prevent the outbreak of infectious diseases.2.Considering that the control of infectious diseases depends not only on the number of infected individuals,but also on the change rate of infected indi-viduals.Therefore,we establish a nonlinear threshold Filippov system with me-dia influence,which incorporates the change rate of infected individuals into the threshold strategy.The main results reveal that the proposed threshold strategy can induce complex dynamic behaviors,including multiple sliding segments and pseudo-equilibrium.In addition,our main results show that the change of thresh-old(E_T)and nonlinear threshold control strategy not only lead to rich dynamics including bistability,but also have important significance for disease control.At the same time,media coverage can reduce the burden of disease outbreaks and shorten the duration of disease outbreaks.