Analysis of stability and Hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells

A delay differential mathematical model that described HIV infection of CD4+ T-cells is analyzed. The stability of the non-negative equilibria and the existence of Hopf bifurcation are investigated. A stability switch in the system due to variation of delay parameter has been observed, so is the phenomena of Hopf bifurcation and stable limit cycle. The estimation of the length of delay to preserve stability has been calculated. Using the normal form theory and center manifold argument, the explicit formulaes which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.