Dynamic Analysis On A Class Of Delay HIV Model With Saturation Infection Rate And Total Logistic ITEM

In this paper, we study a class of delay HIV model with saturation incidence rate and total Logistic item, and discuss the existence and uniqueness of equilibrium points and its stability. Firstly, the relevan-t background and research status about HIV are briefly introduced. Then we give the delay HIV model to be discussed. Secondly, we introduce the concept of delay differential equation and its stability definition, and some stability theorems of the corresponding system are given. Finally, we analyze the stability of HIV model at the e-quilibrium points.And by using the Routh-Hurwitz criteria and some related theorems, we obtain the uninfected equilibrium point is locally asymptotically stable and prove the existence of the threshold τ0, the infection equilibria is locally asymptotically stable as τ< τ0; the in-fection equilibria is unstable as τ> τ0; it appears a Hopf bifurcation in the system as τ> τ0 passing through τ= τ0.