Stability Analysis Of Dengue Model About Within-host Covert Infection

In this thesis,based on the affecting process of dengue,we establish a model about dengue,in which within-host covert infection and vector variety population are both con-sidered,as well as another dengue dynamical model about within-host covert infection and vector vertical transmission,the dynamical properties and biological meanings of each model are discussed.In Chapter 1,we introduce the epidemic of dengue,the background of dengue and the current research status of the dengue dynamical models at home and abroad.Meanwhile some basic theory are briefly stated.In Chapter 2,we study a model about dengue,in which within-host covert infection and vector variety population are considered.Firstly,we prove that the feasible region of the model solution is a positive invariant set and a compact attractive set,and then calculate the basic regeneration.Secondly,we discuss the existence of the equilibria of the model.By proving that the disease-free equilibrium point is locally stable and globally attractive,it is global and stable.Combined with numerical simulation,we prove the possibly locally stability of the positive equilibrium point.We discuss the influence of covert infection parameters on the dengue infection in the end.In Chapter 3,we study a dengue model about within-host covert infection and vec-tor vertical transmission.First of all,the reproductive numbers of the bacteria are com-puted and we discuss the existence of the equilibria.Secondly by constructing a Lya-punov function and combining with the Lasalle invariable principles,the disease-free equilibrium is shown to be globally asymptotically stable.Moreover,by using second additive compound matrices,we obtain the conditions of the globally asymptotical sta-bilities of the endemic equilibrium.In the last chapter,we make a brief review of the above conclusion,and present the practical meaning of these models.And we analyze some shortcomings of this thesis and point out some questions and future work.