Stability Of Viral Immune Models With Diffusion And Time-lag Effects Diverges From Hopf

In this paper,the dynamic behavior of a Simian immunodeficiency virus(SIV)model with diffusion and time delay effects is studied.By using comparison principle,LaSalle's invariance principle and Hopf bifurcation theory,we discuss the basic properties of the solution,the stability of the equilibrium point and the Hopf bifurcation of the SIV model.The main contents of this paper are as follows:The first Chapter is the introduction,which mainly introduces the historical background?research meaning and research status of virus models,and the development status of Simian immunodeficiency virus infection model.Finally,the main research contents of this paper are briefly introduced.In Chapter 2,we study the basic properties of the solution,the stability and Hopf bifurcation of a SIV infection model with diffusion and time delay under homogeneous Neumann boundary conditions.Firstly,the basic properties of the solution of the model,such as the nonnegative,the boundedness,the existence and uniqueness are proved.Secondly,the basic reproductive number R0 and immune reproductive number R1 of SIV are obtained through mathematical analysis,and it is proved that the values of R0 and R1 completely determine the global dynamic behavior of the model.The results show that if R0?1,then the infection-free equilibrium is globally asymptotically stable,and the virus can not continuously infect the host cell and will die out;If R0>1 and R1?1,then the immune-free equilibrium is globally asymptotically stable;If R1>1,then the internal equilibrium is globally asymptotically stable.Both of these later cases indicate that the virus persists in the host cell.Then,the local stability of the internal equilibrium point is established by analyzing the corresponding characteristic equation with the time delay ? as the bifurcation parameter.Moreover,Hopf bifurcation theory is used to study the existence of Hopf bifurcation,and the formula to determine the direction and stability of Hopf bifurcation are given.Finally,numerical simulations are used to verify the above theoretical results.The results show that:for the model given in this paper,the combination of time delay and diffusion will destroy the stability of the internal equilibrium point,and the change of delay will affect the existence of Hopf bifurcation.