Bifurcation and Stability Analysis of HIV Infectious Model with Two Time Delays

The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4+ T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4+ T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4+ T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.