Of A Class Of Local Stability And Hopf Bifurcation Delay Virus Model

In this paper, a viral model with delay is investigated, the stability of the two equilibria is obtained. The general formula for bifurcation direction of Hopf bifurcation is calculated.The delay bound τ0 of the delay differential equation at the positive equilibrium point is given. With the suit parameter condition, τ0 will be the bifurcation value of Hopf bifurcation. With the parameter datum of the [2], τ0 is obtained concretely.A brief arrange of the organization of the paper as follows.The first chapter introduces the charactericteristic equation for differential equations with delays and some fundamental definitions and theories as well as elementary tools.In chapter 2,A viral model with delay is investigated using the theory listed in thapter 1.The conditions of the stability are obtained . The conditions are brief and practical algebraic criterions .Furthermore.we gel the delay bound .The general formula for bifurcation direction is calculated,and the estimation formula of the period for periodic soluttion is discussed using Hassard method.In chapter 3,given an example,we test the frontal formulae .