| As the important infectious diseases in the world,AIDS and hepatitis B,have been seriously harmful to human health.In this paper,we study the dynamic behavior of HIV-1 and HBV infection system by analyzing the stability of the equilibria of corresponding differential equations.This paper mainly discussed the following contents:In chapter 1,the research background and significance of infectious diseases,the research trends of HIV-1 and HBV infection systems,the content and theorems of this paper are simply explained.In chapter 2,we investigate the dynamics of a five-dimensional virus model incorpo-rating CTL immune response,saturation incidence rate and three time delays.Firstly,the basic properties of the model are introduced,including the well-posedness of solutions,as well as basic reproduction number and existence of the equilibria.Secondly,by analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcation are established,respectively.Thirdly,by using fluctua-tion lemma and constructing suitable Lyapunov functionals,it is shown that the first two equilibria are globally asymptotically stable under local stable conditions.Finally,some numerical simulations are carried out for illustrating the theoretical results.In chapter 3,we study the dynamics of a new chronic HBV infection model that includes spatial diffusion,general incidence function and three time delays.First,we analyze the well-posedness of the initial value problem of the model in the bounded domain.Then,we define a threshold parameter called the basic reproduction number and show that our model admits two possible equilibria.Further,by constructing two appropriate Lyapunov functionals,we prove that the global dynamical behavior of each equilibrium point is completely determined by the threshold of the system.In the end,some numerical simulations are provided to illustrate the main results in the previous section. |
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