Analysis Of A Kind Of Vector Borne Infectious Disease Model With Media Influence

Media report is the media collect information through a series of reliable channels,and then inform the public through network,television,newspaper and so on.Thus when a disease occurs in social life,the media will be more likely to inform the public the information of disease at the first time.This allows the public to have a certainunderstanding of the disease,and make them react accordingly to reduce their chances of being infected by the disease,which greatly mitigate the spread of infectious diseases.Based on this understanding,this paper establishes a kind of media infectious disease model related to media coverage.This article uses a monotonically decreasing function h(x)to describe the impact of media coverage on the spread of the disease.Here the function h(x)is called the media function and its monotone decreasing character-istic is determined by the following reason.When disease outbreak,the media will inform the public about the extent of the outbreak and the prevention measures of the disease.The public will make appropriate behavior to reduce the risk of infectious disease after they obtain relevant information,which may reduce the infection rate.In the theoretical analysis,the existence and uniqueness of the equilibrium and its stability are discussed.In the discussion of the local stability of the endemic equi-librium,the condition of the Hopf bifurcation is also obtained.By constructing the Lyapunov function,the global stability of the disease-free equilibrium point is proved.In the model,we introduce a class of general functions,so we need to add a condi-tion when the Lyapunov function is useed to prove the global stability of the endemic equilibrium point.Finally,we take the specific form of the general media function.On the one hand,we use concrete examples to verify the theoretical results of this paper.On the other hand,a class of piecewise smooth functions is selected to investigate the parameters which are directly related to the media coverage.The existence condition of Hopf bifur-cation are found and the shock graph is obtained through simulation.By applying the Lambert W function to convert the system into a switch system,we derive the switch surface and the existence of the equilibrium for the two subsystems.