A Delayed HIV Infection Model with the Homeostatic Proliferation of CD4^(+)T Cells

In this paper,we investigate a delayed HIV infection model that considers the homeostatic prolif-eration of CD4^(+)T cells.The existence and stability of uninfected equilibrium and infected equilibria(smaller and larger ones)are studied by analyzing the characteristic equation of the system.The intracellular delay does not affect the stability of uninfected equilibrium,but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles.Furthermore,direction and stability of Hopf bifur-cation are well investigated by using the central manifold theorem and the normal form theory.The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay.Moreover,when the maximum homeostatic growth rate is very small,the larger positive equilibrium is always stable.On the contrary,when the rate of supply of T cells is very small,the larger positive equilibrium is always unstable.