Study On The Dynamics Of HIV-1 Virus Influenced By Age Structure

By establishing a reasonably and accurately epidemic model,people can effectively research and analyze the spread of infective disease,and infective diseases can be effec?tively prevented and controlled.With the deep studies of the epidemic model,people have found that some infectious diseases are related to the age of human beings.The infection age of infected cells is different and the ability to produce the virus is different,which leads to the change of the dynamic of the HIV-1 infection model.Thus,it is of great theoretical significance to study the HIV-1 infection model with age structure.In this paper,it mainly study the analysis of HIV-1 infection model with age-structured and target cell growth by logistic and stability analysis in an age-structured HIV-1 infection model with mitosis transimission.The thesis consists of five chapters.In the first chapter,it mainly introduces the history of the development of HIV-1 and progress in this field so far,as well as the significance of studying the HIV-1,and simply introduce the problems we study in this paper.The second chapter mainly gives some preliminary knowledge that is used in the article.The third chapter establishes the age structure model of two HIV-1 infection modes(cell-to-cell and virus-to-cell)and the target cell is Logistic growth.Considering the dy-namic behavior that the equilibrium depends on the basic reproduction number.The consistent persistence of the system is obtained by using the consistent persistence the-ory of the dynamic system.The positive and uniqueness of the infection equilibrium,the boundedness of the system solution satisfying the initial conditions are proved,and the stability of the uninfected equilibrium of the model is analyzed,and the sufficient conditions for the global asymptotic stability of the uninfected equilibrium are obtained.The fourth chapter studies a class of infected cells and uninfected cells with HIV-1 age structure model of mitosis and proliferation.Considering the posedness of the model.And it is proved that if the basic reproduction number is greater than 1,only infection equilibrium exist,and the stability of the infection equilibrium is analyzed by using Routh-Hurwitz criterion and correlation theorem to judge the sign of the eigenvalue.Specifically,when the basic reproduction number is less than 1,the disease-free equilibrium is globally asymptotically stable,and when the basic reproduction number is greater than 1,the uninfected equilibrium is unstable,but the infection equilibrium is locally asymptotically stable under certain conditions.The fifth chapter:Summary and outlook.