Analysis Of Stability And Persistence For A HIV Infection Model

Although some infectious diseases are controlled and prevented effectively with thedevelopment of scientific and medical, there are still many infectious diseases harm tohuman beings health seriously. In recent years, more and more scholars pay attention tothe study of infectious diseases by use differential equations. In this paper, we firststudy the stability and persistence for a HIV infection model with time delay andnonlinear infection rate,after that study the stability of HIV model with impulsive ofimmune factorThis paper is composed of four chapters.In first chapter, the background, signification and evolving of AIDS are brieflyreviewed. Furthermore, we simply introduce the main work in this paper.In the second chapter, a HIV model with time delay and nonlinear incidence rate isinvestigated. By the reproduction numbers and the character equations, we first analyzestability of the disease-free equilibrium, and then give the relation of stability of theendemic equilibrium between the model without delay and one with time delay. At last,we obtain some sufficient conditions ensuring the uniform persistence of the model byusing the persistence theory.In the third chapter, study on a stability for a HIV model with impulsive immunefactor. Using the impulsive differential inequality and comparative theorem, the authorsinvestigate the existence of infection-free periodic solution of the impulsive HIV system,and then discuss the stability of the infection-free periodic solution of HIV.In the fourth chapter, I know a little about HIV, on the further day I must to dosome knowledge about the HIV.