Stability Analysis Of Two HIV Infection Models With Logistic Growth

HIV is a retrovirus that can attack the human immune system,which has high pathogenicity and fatality rate,and seriously endangers the security of human life.Be-cause there is no vaccine and perfect treatment,finding the best treatment has become one of the focus issues of the world.The method of virus dynamics has unique ad-vantages in understanding the pathogenesis of diseases and predicting its development trend,which can provide new insights for disease prevention and control.In this thesis,two delay HIV infection dynamic models with Logistic growth are established,and their dynamics are analyzed.The effects of factors such as virus generation delay,infection delay and immune delay on the dynamics of virus infection in vivo are studied,and their biological significance is explored.In the first chapter,the background knowledge of HIV and the relevant research progress of HIV infection dynamic models are introduced,the main work of this thesis is explained.In the second chapter,a dynamic model of HIV infection is established,which con-siders healthy T cell self-proliferation,two mechanisms of HIV infection,CTL immune delay and CTL immune impairment.Firstly,nonnegativity and boundedness of the so-lutions are proved.Secondly,the basic reproductive number for viral infection R0 and the basic reproductive number for immune response R1 are defined,and the existence of the equilibria are obtained.Thirdly,stabilities of the equilibria are studied by us-ing the Hurwitz criterion,the suitable Lyapunov functions and the LaSalle's invariance principle.And then,conditions for Hopf bifurcation to occur are given.Finally,the influence of immune impairment term on the dynamic behaviors of the system is studied by numerical simulations.The results show that the CTL immune delay will lead to the production of Hopf bifurcation,and the immune impairment will aggravate the infection of the virus.Based on the model in Chapter 2,in Chapter 3,the effects of virus generation delay and infection delay on the dynamics of virus infection in vivo are further considered,and the two delays are considered as distributed delays.The effect of cell-to-cell infection is ignored and the bilinear incidence rate is replaced with a more biologically signif-icant saturation incidence rate.In this chapter,nonnegativity and boundedness of the solutions are proved,the basic reproductive number for viral infection R0 and the basic reproductive number for immune response R1 are defined and the global stabilities of the equilibria are analyzed.Only in the presence of the CTL immune delay,conditions under which Hopf bifurcation occurs are investigated.The results show that the virus generation delay and infection delay have no effects on the stabilities of the equilibri-a.The immune delay will affect the stability of the infection equilibrium.When the immune delay is greater than a certain critical value,the infection equilibrium becomes unstable state from the stable state,and the system has a Hopf bifurcation.In the fourth chapter,the main work and shortcomings of this thesis are pointed out,and the work worthy of further study is put forward.