Global Analysis Of Several HBV Mathematical Models

In this paper,we mainly study the dynamics of some HBV mathematical systems.The article includes four chapters.The preface is in chapter 1,we introduce the research background of this article,the main task and some important preliminaries.In Chapter 2,we construct a class of HBV mathematical model that contains virus capsid,the cure rate and intracellular absorption effect.Firstly,by using the method of characteristic and the Routh-Hurwitz criterion,we discuss the local stability of the disease-free equilibrium and the epidemic equilibrium.Then,the global stability of the disease-free equilibrium is proved with the help of appropriate Lyapunov function.In the end,numerical simulations are carried out to explain the mathematical conclusions.In Chapter 3,we build a model of HBV with diffusion term and the infection and prolifer-ation of viruses which are related to its quantity.In this system,the infection rate of the disease is expressed by the Crowley-Martin response function.Firstly,We investigate the positivity,boundedness of the solutions and the existence of the equilibria of this system.Then,the local stability of the free equilibrium is proved by the method of characteristic under the Neumann boundary conditions.We also showed the global stability of the disease-free equilibrium and the endemic equilibrium by the appropriate Lyapunov function and the LaSalle's invariance principle.In Chapter 4,we propose a disease model with piecewise incidence function and piecewise treatment function.First of all,this chapter analyzes the existence of positive equilibrium point when the number of patients is less than the maximum capacity of medical resources under the influence of media.Also,by analyzing the characteristic equations,the local stability of disease-free equilibrium and the endemic equilibrium of the model are established.Secondly,the system is discussed in a similar way without the media impact.Finally,with the help of Bendixson-Dulac criterion,it is proved that the system does not exist limit cycle when the number of patients dose not exceed the maximum intake capacity of medical resources.When certain conditions are established,the disease-free equilibrium and the endemic equilibrium are globally asymptotically stable.