Dynamics Of A Class Of HIV-1 Virus Models With General Function Terms

AIDS is one of the important topics in the field of public health research.It is a very infectious diseases caused by the HIV virus that attacks the human immune system.At present,the spread of HIV in the host has been shown to exist in two different mechanisms,virus-to-cell infection and cell-to-cell transmission.Based on the two mechanisms of virus-to-cell infection and cell-to-cell transmission,consider the non-linear general incidence rate,general mortality,intracellular distribution delay and CTL immune responses,a novel four-dimensional HIV-1 virus model was established in this paper,and its dynamic behavior was analyzed.Specifically the following works were carried out:The first chapter introduces the research background of virus dynamics and the pathogenic principle and clinical background of AIDS disease.Summarizes the research status and development of the current HIV-1 virus model,and puts forward the research content and main work of this paper.The second chapter establishes four-dimensional HIV-1 virus model,based on the two mechanisms of virus-to-cell infection and cell-to-cell transmission of HIV-1 virus,considering the general incidence of nonlinearity,general mortality,intracellular delay and CTL immune responses.It is convenient to study the model,put forward eight basic hypotheses,and introduce the relevant preliminary for studying the model.In the chapter three,on the basis of giving three thresholds(R0,RV and RCTL)suitable for studying the model of this paper,the existence and uniqueness of the three equilibrium points of the four-dimensional HIV-1 virus model(infection-free equilibrium,the CTL-inactivated equilibrium and the CTL-activated equilibrium)were demonstrat-ed.The stability of the three equilibrium points is given by the appropriate Lyapunov functionals.The fourth chapter is to illustrate the universality of the four-dimensional HIV-1 virus model and its conclusions.The general function term in this model is embodied,and four application examples of this HIV-1 model were established,(1)an HIV-1 model with Logistic growth,two infection mechanisms and saturated discrete delay,(2)an HIV-1 model with bilinear discrete delay,(3)an HIV-1 model with saturation discrete delay and(4)an HIV-1 model with two infection mechanisms and bilinear distribution delay.The fifth chapter summarizes the main research contents and conclusions of this paper and puts forward some related work that needs to be further carried out in the future.