Considering A Dynamic Model Of HIV-1 Infection With Multiple Influencing Factors

AIDS is an infectious disease caused by human immunodeficiency virus and characterized by severe damage to the whole immune system.The main pathogen causing the disease is HIV-1.The dynamics of the HIV-1 infection model is very useful in the control of infectious diseases,and provides ideas for the study of the dynamics of the viral load in the body.The analysis of these dynamic behaviors may play an important role in better understanding AIDS and the development of various drug treatment strategies.In this thesis,many factors that affect the dynamic behavior of HIV-1 infection are considered,and a dynamic model of HIV-1 infection with multiple factors is established.The mathematical conclusion and biological significance are analyzed and discussed.In the first chapter,the background and significance of HIV-1 research are briefly introduced.And the current research situation of HIV-1 virus infection model with different influencing factors and the research content of this thesis are analyzed.In the second chapter,it is established and studied for a double discrete timedelay HIV-1 model with cell-cell infection,humoral immunity and RTI.Firstly,The nonnegativity and boundedness of the system solution is proved by using the theory of differential equations,and then the existence of the equilibrium points of the system are proved by using the basic reproduction numbers 0,1.Secondly,the local stability of the equilibrium points of the system are proved by calculation.Then,by constructing suitable Lyapunov functional,the global stability of the equilibrium points are proved.At the same time,the existence of Hopf bifurcation is proved by analying.Finally,using numerical simulation shows that when time delays and the effectiveness of the reverse transcriptase inhibitor(RTI)takes the different values,the system stability Changes,the correctness of the theory is verified.It is found that the intracelluler discrete time delays does not affect the dynamic behavior of the system.But the delay of immune generation has an important influence on the dynamic behavior of the system.When the delay of humoral immune generation exceeds a certain threshold,the system will change from stable state to unstable state.And this transformation is generated by the system through Hopf bifurcation.It is also found that only when the delay of humoral immune generation is large,the system can generate periodic oscillatory solutions through the Hopf bifurcation.Further research shows that when the effectiveness of the reverse transcriptase inhibitor(RTI)is not zero,that is,when the drug is effective,the system will reach a stable state even if there is a delay in humoral immune production.In the third chapter,on the basis of the model in the second chapter,to observe the dynamics of the system,virus-cell infection delay and cell-cell infection delay are considered as different delays.At the same time,virus generation delay is introduced.The original discrete delays are considered as distributed delays.Therefore,the dynamic model of HIV-1 infection with multiple factors was established and studied.By using differential equation theory,Lyapunov functional theory,the thesis proves in turn the nonnegativity and boundedness of system solutions,the existence of equilibrium points,the global stability of equilibrium points.And through discussion and analysis,the existence of Hopf bifurcation is proved.At last,the change of the stability of the system when the four delays are different is obtained.It is found that although virus-cell infection delay that is different from cell-cell infection delay and the introduction of virus generation delay will not affect the dynamic behavior of the system.However,the longer virus generation delay is,the longer the system tends to be in equilibrium.In the fourth chapter,this thesis reviews the previous work and main conclusions and discusses the shortcomings of this work and the problems and work that need further study.