Dynamic Behavior Analysis Of Multi-Scale Nested Immune-Infectious Disease Models In HIV/AIDS Research

In recent years,AIDS has become one of the major public health problems threatening human health.It has the characteristics of rapid epidemic and high case fatality rate.There is currently no cure,which has important implications for socio-economic development and stability.Chinese governments and departments at all levels have been paying close attention to the spread and prevention of HIV/AIDS.By analyzing the relationship between HIV transmission mechanism in host and AIDS in host,a new nested immune-infectious disease model is established.The stability of the new model is analyzed to provide more reasonable suggestions for the prevention and control of AIDS.The main contents of this paper are as follows:In Chapter 1,the background and current status of HIV dynamic model and AIDS infectious disease model are introduced,and the research value and significance of multi-scale nested immune-infectious disease model in HIV/AIDS research are clarified.In Chapter 2,we present some concepts of stability theory and research methods needed in the study of infectious diseases.In Chapter 3,a dynamic model of HIV virus infecting CD4+T cells with Logistic mitosis and inhibiting the production of CD4+T cells in vivo is studied.By using Routh-Hurwitz discriminant method,LaSalle invariance principle and Li-Muldowney geometric method,we discuss the global stability of the model and obtain the conditions for the global asymptotic stability of the HIV infection equilibrium point.In Chapter 4,on the basis of Chapter 3,we introduce the CD4 + T cells by Logistic increased mitotic cause infected cells,immune reaction can be restored to uninfected status and CTL immune response in the antibodies to the virus particle removal effect and other factors,based on the HIV infection of CD4 + T cells and infection cells infected CD4 + T cells,the two mechanisms of infection,virus dynamics model is established.Stability of disease-free equilibrium point was analyzed by Routh-Hurwitz discrimination and LaSalle invariance principle.By means of Li-Muldowney geometric method,the global asymptotic stability condition of the positive equilibrium point is obtained when the fundamental regeneration number is greater than 1.In chapter 5,according to the relationship between HIV transmission rate in the population and the virus carrying variables in individuals,we established a multi-scale HIV infection dynamics model based on CVL by introducing a specific community viral load(CVL)and combining the micro host immunodynamics model with the macro SIATR epidemiological model.Finally,the global stability of the multi-scale nested model is analyzed by means of LaSalle invariance principle.In chapter 6,combined with the contents of the first five chapters,this paper summarizes the main results of the immune-infectious disease model of AIDS.