Dynamic Of HIV Infection Modelwith Time Delay

In recent years, it gives our lives not only a lot of convenience, but also manyproblems with social development and advances in science. For example, a variety ofinfectious diseases, such as influenza epidemic has impacted on people’s lives. AIDS isso. There are many extensive researches about the mechanism of HIV causing AIDS indifferent areas. It presents a mathematical model of HIV infection, because of itsimportant theoretical and practical significance. Through mathematical model, we canunderstand the dynamics of viral load and it is also helpful for clinic treatment.In this paper, we discuss the stability and the Hopf bifurcation of the HIV infectionmodel with time delay, which is primarily by target cells, infectious target cells and thevirus capacity to describe. In the model, time delay accounts for the time between viralentry into a target cell and the productions of new virus particles.Delay in the range of the equilibrium point for the stability of the system has greatinfluence.First, we consider the existence of two equilibrium points, such as free of virusequilibrium point and viral equilibrium point, and discuss local stability using the linearmethod and the Routh-Hurwitz criterion. We prove the global stability of boundaryequilibrium point by LaSalle invariance principle. Secondly, we get the formula of Hopfbifurcation direction and stability. Finally, we use the mathematical software Matlab tocarry out the numerical simulation and draw the corresponding waveform diagram andphase diagram to support theoretical results. We can find that with the change of timedelay, the system has “switch” phenomenon and when it reaches a critical value, thepositive equilibrium point does not exist. The specific interval for delay has effect onchanges of system stablity.