Stability And Bifurcation For Two Types Of Dynamic Models With The Impact Of Media

The modern society is an era of rapid development of information technology,and the speed of information dissemination is faster than ever.While information transmission invisibly changes people's lifestyles,it also has a non-negligible influence on the spread of infectious diseases.Positive and negative information play a different role during the epidemic.To study the role of positive and negative information in the dynamics of infectious diseases,this paper constructs two models with media.Using the relevant theory of ordinary differentials,we analyzed the models:First,A SEIS infectious disease model with media information was established and the model was analyzed for dynamics.By mathematical analysis,we obtained the basic reproduction number for the existence of endemic equilibrium.By constructing Lyapunov functions,we proved the globally asymptotic stability of disease-free equilibrium.The existence and stability of endemic equilibrium are proved.The occurrence of a forward,backward and Hopf bifurcation is derived.Numerical simulations and sensitivity analysis indicate that during epidemic infections,the spread of infectious diseases and the number of infected people will reducing as negative information is reducing or positive information is increasing.Then,A SIS infectious disease model with media information was established and the model was analyzed for dynamics.We provide the basic reproduction number and prove the local asymptotic stability of disease-free equilibrium.The existence and stability of endemic equilibrium are proved.The occurrence of a forward,backward and Hopf bifurcation is derived.Numerical simulations and sensitivity analysis indicate that media can regard as a good indicator in controlling the spread of the epidemic disease during epidemic infections...