The Analysis Of Two Classes Of Mathematical Models For Dengue

In this paper,we mainly study the dynamics of two classes of dengue mathematical models.The article includes three chapters.The preface is in chapter 1.we introduce the research background of this article and list some important preliminaries.In Chapter 2,a six-dimensional mathematical model is constructed and analyzed for the transmission of dengue fever.Firstly.the conditions for the existence and local stability of five boundary equilibria are obtained.Secondly,the existence and local stability of the positive equilibrium are studied.At the same time,the sufficient conditions for the occurrence of Hopf bifurcation are also arrived.Thirdly,by adding a control variable into the original model,optimal control strategy is considered.By applying the Pontryagin’s Maximum Principle,the optimal solution is obtained.In Chapter 3.an impulsive model with delays is proposed to study the spread of dengue fever.Firstly,we get the sufficient.conditions for the global attraction of the infection-free periodic solution.Then,the sufficient conditions for the persistence of the disease is obtained.