Stability and Hopf bifurcation analysis of a HTLV-Ⅰ infection model with time-delay CTL immune response

This paper is devoted to proposing a mathematical model in order explore the dynamics of HTLV-Ⅰ (human T-cell leukemia virus type-Ⅰ) infection, which closely related target cell-virus-immune system interaction and time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give relevant lemma for existence feasible equilibrium points model, then further certify global asymptotic stabilities infection-free (IFFE) $ E_1 immune-free (IMFE) E_2 $. Furthermore, research Hopf bifurcation (HB) occurring at (IE) E^* due influence delay parameter. Also, numerical simulations confirm this fact. In addition, obtain explicit expressions determine direction stability HB. Finally, succinct discussion shows that CTL can destabilize generate HB, but not affect