Dynamic Behavior Of HIV Infection Models With Intracellular Delay,CTL Immune Response And Immune Impairment

Human immunodeficiency virus(HIV)is a kind of retrovirus which spreads widely and causes strong pathogenicity.HIV mainly attacks CD4+ T cells in the human immune system,causing the gradual collapse of the human immune system,eventually leading to the host infection with Acquired Immunodeficiency Syndrome(AIDS).HIV infection usually induces a specific immune response in the host,and cytotoxic T lymphocyte(CTL)mediated cellular immunity plays a key role in controlling viral load in the host by inhibiting virus production and lysis of infected CD4+ T cells.In addition,CTL immune response can be inhibited or destroyed when the antigen load in the host body is too high.Therefore,it is very important to study the effects of intracellular delay,CTL immune response and immune impairment on the dynamics of HIV infection.Based on this,this paper studies the following contents:In Chapter 1,the background,significance,status and main works of this paper are introduced.In Chapter 2,an HIV infection model with intracellular delay,CTL immune response,immune impairment is established.The basic reproduction ratio of virus infection is obtained by using the next generation matrix method.By analyzing the distribution of the roots of the corresponding characteristic equation,the local asymptotic stability of the feasible equilibria are proved.By constructing appropriate Lyapunov functionals and using LaSalle’s invariance principle,we prove that when the basic reproduction ratio of virus infection is less than 1,the virus infection-free equilibrium is globally asymptotically stable,and when the basic reproduction ratio of virus infection is greater than 1,the virus infection equilibrium is globally asymptotically stable.Finally,the parameter sensitivity of the basic reproduction ratio of virus infection is analyzed.In Chapter 3,a delayed-within-host HIV infection model with cell-to-cell transmission,mitotic proliferation,CTL immune response and immune impairment is established.The basic reproduction ratio of virus infection is obtained by using the next generation matrix method.When the basic reproduction ratio of virus infection is greater than 1,the mitotic proliferation rate of susceptible target cells and intracellular delay are taken as bifurcation parameters respectively,and the conditions for the system to generate Hopf bifurcation and the stability switch phenomenon at the virus infection equilibrium are given.Furthermore,by using the center manifold theory calculates the normal form,the conditions that determine the Hopf bifurcation direction and stability of bifurcation periodic solution are obtained.In addition,by constructing appropriate Lyapunov functionals and applying the LaSalle’s invariance principle,the conditions for the global asymptotic stability of the virus infection-free equilibrium and the virus infection equilibrium are proved respectively.Finally,the parameter with critical influence on the basic reproduction ratio of virus infection is determined by the parameter sensitivity analysis.In Chapter 4,we summarize the research work of this paper and propose the target of future research.