Bifurcation Analysis On Several HIV Models

AIDS is a kind of dangerous diseases to human body,caused by human immunodeficiency virus(HIV).HIV is an RNA virus that at-tacks the human immune system.HIV targets CD4+T lymphocytes in the human immune system,and the human body gradually loses its immune response,which makes the body susceptible to various diseases and cause malignant tumor,the fatality rate is very high.Therefore,it is very important to study the mechanism of HIV infec-tion and to control the transmission of AIDS.This paper mainly studies the local dynamics and global dynamics of three AIDS related models,and it is divided into the following five chapters.In the first chapter,we firstly describe the harmfulness of AIDS to human body and the mechanism of HIV infection,and introduce the research progress of HIV infection models in recent years.Then it mainly introduces the work done in this dissertation.Finally,the basic definitions and theorems are also given.In the second chapter,we study a three-dimensional HIV system with cell-to-cell interaction,which includes uninfected T cells,infected T cells and HIV viruses.Firstly,the existence of the equilibrium,sta-bility and bifurcation are analyzed for the model.Then the influence of infection rate among cells on the existence of equilibrium point and Hopf bifurcation point is illustrated by numerical simulations,and the existence of BT bifurcation and homoclinic orbit are given.In the third chapter,we study local and global bifurcation in a four-dimensional HIV model with vectored immunotherapylaxis and cell-to-cell transmission.Through theoretical and numerical analysis,various dynamic behaviors are studied,including backward bifurca-tion,Hopf bifurcation,homoclinic bifurcation,Bogdanov-Takens bi-furcation,hysteresis and isola bifurcation.The isola bifurcation of pe-riodic orbits is first detected numerically in HIV model,which means that there is a parameter interval with the same oscillations.It is shown that the effect of vectored immunoprohylaxis in this model is the main cause of the periodic symptoms in HIV disease.Moreover,it is also shown that the increase of cell-to-cell transmission may be the main factor causing Hopf bifurcation to disappear,and thus elim-inating oscillation behaviour.In the fourth chapter,we first study a 5-dimensional ODE system with cell-to-cell infection when HIV virus mutates,and analyse the existence and stability of the equilibrium point of this system.It was then extended to a 10-dimensional ODE system containing CD8+T cells,the existence of the equilibrium point is analyzed,and the effect of drug on HIV are analyzed through optimal control.It is shown that,the effect of FI on increasing CD4+T cell concentration is more significant than that of RTI because of the consideration of HIV mutation in this chapter,which was different from the HIV model without consideration of virus mutation.The fifth chapter is a summary of the above research results,and we also propose the future research direction.