The Studies Of HIV-1 Virus Dynamic Models With Latent Infection And Immune Response

Acquired Immune Deficiency Syndrome?AIDS?is a very dangerous infectious disease caused by Human Immunodeficiency Virus?HIV?infection.HIV virus can invade T lymphocytes and macrophages of the human immune system,such that the function of human immune is missing.Therefore,it is of great practical significance to study the dynamic behavior of HIV virus with latent infection and immune re-sponse in the antiviral treatment and prevention of HIV.This thesis mainly studies the following contents in combination with the biological phenomena of virus dy-namics model such as immune response,time delays and latent infection reservoirs.Firstly,we study an HIV-1 virus infection model with antibody immune re-sponse and cure rate.The model not only considers the infected cells at the latent stage,but also considers that the infected cells in the incubation period can be cured and transformed into susceptible CD4⁺T cells.The global stability of HIV-1virus infection model is deduced by using Lyapunov functions for infection-free equi-librium,immune-free equilibrium and antibody-activated equilibrium under certain some conditions.In addition,the numerical simulation to verify the global stability of immune-free equilibrium and antibody-activated equilibrium,respectively.Secondly,we consider a delayed HIV-1 virus model with antibody immune response and virus waning term.According to the theory of differential equation,we prove that the positiveness and boundedness of the solution of the system,and the basic reproduction number is given.Moreover,we discuss the effects of the virus waning term.Then,we proved the stability of infection-free steady state at R₀<1.By constructing Lyapunov functional and combining the LaSalle invariant principle,we prove that infection-free equilibrium is both locally asymptotic stability and global asymptotic stability when R₀<1,and when R₀>1,we obtain the local stability of the infected equilibrium and give the conditions of the Hopf bifurcation.Finally,we analyze an HIV-1 virus dynamic model with latent infections and two time delays.we obtain the expression of the basic reproduction number by using next-generation,and caculate the equilibria of the system.Then,we show that the local and gobal stability of equilibria by using Routh-Hurwitz and constructing Lya-punov functionals,respectively.Moreover,The numerical simulation results reveal the effect of time delays on the dynamic behavior of the system.