Discussion On Stability Analysis Of HIV Model With Age-structure

HIV/AIDS is a very harmful immunodeficiency disease,the full name of it is acquired immun-odeficiency syndrome,it attacks the human immune system and makes the body's immune function lost,so the human body gets infected,eventually it makes people dead.Many medical workers and researchers in the world have paid a lot of effort to find a cure for AIDS,however,the proper vaccines have not been found to control the spread of AIDS.With the increasingly daily activities among peo-ple,there is still a tendency for HIV/AIDS to spread further.In our country,the epidemic of AIDS is also very serious.Therefore,the research on AIDS has theoretical and practical significance.There are many factors that affect the transmission of AIDS.By establishing relevant models,we can understand the rule of the transmission.This article will study the HIV/AIDS model with the physiological age and density restriction.The population is divided into three groups susceptible class,infective class and disease class.First,by using the characteristic line method and differential equation theory,the existence and uniqueness of the solution of the system will be discussed.Then by using the theory of the partial differential equation,the existence and.uniqueness of the endemic equilibrium will be proved.Finally the stability of the equilibrium point will be analyzed.