With Time Delays Virus Model Of Stability And Branch

At present ,a lot of delay differential equations exist in many fields in biology and medicine , so delay differential equations have become a subject of important research activity. In this paper, a viral model with delays is investigated, the sufficient and necessary conditions of the unconditional stability at a positive equilibrium point, and the delay bound of the delay differential equation are given. The general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimation formula of the period for periodic solution is obtained.A brief decription of the organization of the paper follows. The first chapter introduces the characteristic equation for differential equations with delays and some fundamental definitions and theories as well as elementary tools . In chapter 2, A viral model with delays is investigated using the theory listed in chapter 1. The sufficient and necessary conditions of the unconditional stability are obtained. The conditions are brief and practical algebraic criterions. Furthermore, I get the delay bound. The general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimation formula of the period for periodic solution is discussed using Hassard method.