Pattern Dynamic Of A Reaction-diffusion Epidemic Model With Media Impact

Epidemic is always a focus of attention by people.In recent years,some sudden diseases,not only make a great threat to human health,but also have a significant impact on the stability of society.For these sudden diseases,effective drugs and vaccines can not be in a short time.Therefore,the most effective measures preventing large-scale outbreaks of diseases is that some experts spread all useful information to people and tell them how to protect themselves from infection.The media influence plays a significant role.Thus,this paper mainly analyzes and discusses the infectious disease model with media influence.In Chapter 2,the diffusion SI model with media effect is established.First,the boundedness of system,the existence of equilibrium points and the local asymptotic stability are obtained from system without considering the reaction diffusion.Then,when the system contains reaction diffusion,by taking the media coefficient as the branching parameter,Turing branch of conditions which under the system occurs are discussed.Finally,we use software Matlab to carry out numerical simulations to verify the rationality of the conclusion.In Chapter 3,we establish the diffusion SIS model with time delay,which is affected by media.First,we prove the existence of equilibriums,positivity and boundedness of the solution of such system.Then we discuss the local stability of boundary equilibrium and positive equilibrium of the system without delay and diffusion term.In the case of diffusion term,we obtain the conditions for the occurrence of Turing bifurcation.When diffusion and delay term are taken into account the system,we show the occurrence of Hopf bifurcation of the system.Finally,numerical simulations are given to explain the theoretical results.