Analysis Of An HIV Infection Dynamical Model With CTL Immune And Antibody Immune Response

AIDS is still a serious infectious disease.It is caused by HIV infection and has resulted in enormous burden to the world.Mathematical modeling has become a powerful tool for studying the control of the spread of AIDS.HIV mainly destroys the body's immune ability and attacks the immune system.Models constructed in the form of time-delay differential equations are often used to study the dynamical behavior between virions,infected cells,immune cells and antibodies within infected individuals.In this paper,we develop and analyze an HIV infection model with latent infection and the immune response.The model includes saturated infection rate,latent infection cells,two time delays,cellular immunity and antibody immunity.The first chapter introduces the research background and significance of studying HIV dynamics.We review the current research of HIV infection with time delays and immune responses using mathematical models.We also summarize the research content of this paper.The second chapter shows the formulation of the HIV-1 virus infection model with latent infection and multiple time delays,as well as the immune response.The differential equation theory is used to prove the non-negativeness and boundedness of the system's solution.We obtain the characteristic equation using the Jacobian matrix and study the local stability of the infection-free and infected steady states.Lastly,we study the global stability of the equilibrium points by constructing the Lyapunov functional and applying the LaSalle invariant principle.The third chapter carries out numerical analysis.Numerical simulations with different sets of parameters have been used to illustrate the stability of the infectionfree equilibrium point,the equilibrium point without immune response,the equilibrium point with CTL immune response,the equilibrium point with antibody response,and the equilibrium point including both two types of immune responses.Lastly,we perform numerical simulation to study the effect of time delays on the HIV dynamics.