Stability Analysis Of Two HIV Models With Stage-structure

Since AIDS(acquired immune deficiency syndrome)was first discovered in the United States in the early 1980s,the human immunodeficiency virus(HIV)has spread rapidly around the world and soon spread to all continents,seriously endangering human health.According to the latest data released by the ministry of health,AIDS has become one of the highest death rates of infectious diseases,and its major threat to human life security has attracted the attention of the world health organization and relevant government departments around the world.Therefore,the study on the mechanism of HIV infection,the law of transmission and the prevention strategy has become one of the hot topics for doctors,biologists and mathematicians in various countries.In general,differential equation models are established to study the changing rules of the HIV infection model over time,and age-structure and stage-structure are added to analyze the systematic mechanism and treatment plan.Firstly,this paper introduce briefly the current status of the development of HIV models in the field of biological mathematics.Secondly,study a class of mutiple delays HIV infection with stage-structure excluding effector cells,the paper convert three delays problem into a double delay,calculate the characteristic equation of the positive equilibrium point,and study its feasible region,the stable switching curve and switching direction using geometric method,furthermore,the influence of time delay on the stability of the model is analyzed.Because the HIV is a chronic virus,it can infect the human immune system,the virus causes the destruction of the body's own immune system mainly by infecting CD4~+T cells and CD8~+T cells in the body.So the article on the basis of the classical HIV model considering the double delay HIV infection model with the effector cells and stage-structure.The paper calculate the characteristic equation of the positive equilibrium point,discuss the feasible region,the stable switching curve and switching direction using geometry method.The stability of the model is analyzed when multiple time delays change simultaneously and some specific numerical examples are given to illustrate the correctness of the results.